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Talk:Recumbent bicycle

Untitled
A picture would be helpful. -Frecklefoot

Isn't it possible to exert more force while peddling a recumbent bike, as you are able to brace against the seat, whereas in a normal bike the force you exert can never be greater than your weight? --Neil

I noticed a discrepancy betweent this page and the bike page. The bike page quotes a much higher speed record for a rcubet bicycle set by a Canadian. I don't know enough to determine who is right but maybe the discrepancy should be addressed? -- Fred

Recumbent bikes sound cool! - a guy

Expanded a bit, removed some probable vandalism, structured a bit. More needed on recumbent culture (and, IMO, on the competition scene) Just zis Guy, you know? 12:47, 7 October 2005 (UTC)

 * Question: What does "unpaced" mean, in the context it is used here? I don't understand it, and other sources (google definition, etc) don't supply an answer. 124.171.39.105 (talk) 23:02, 9 January 2008 (UTC)

Recumbents banned from racing
  RecumbentReCycler (talk) 13:06, 25 June 2008 (UTC)

Work in progress by Jus zis Guy
I am working on expanding the History section; I will also incorporate some more info from Gunnar Fehlau's "The Recumbent Bicycle" which is a pretty good authority. - Just zis Guy, you know? 11:56, 8 October 2005 (UTC)

Recumbents for Handicap and elderly
I am post polio with strong upper arms but weak legs in need of exercise. I simply need a low cost multispeed ratio to allow both leg and armpropulsion. Is there any available?? jbaum12@msn.com

Standing on hills
82.143.162.72 11:11, 29 January 2006 (UTC) There are references to the 'disadvantage' of not being able to stand when going up hill. Should there be something in these sections that mentions that it is not energy-efficient to stand when riding an upright? Try doing it when there is snow on the ground and you will feel how little of your pedalling is turned into forward movement and how much is turned into wheel-spin.

 * Think about the question and your example. The reason the wheel slips when the rider is standing, but not when sitting, is because it's pushing harder across the ground than when the rider is sitting. When you're on asphalt, the friction is great enough so that all that extra energy that causes the wheel to slip on ice is used to propel yourself forward. Temple 21:30, 2 February 2006 (UTC)

See the reference in the cycling page to comparative studies on standing vs sitting techniques - more power standing, just as efficient. Standing also move weight off the rear wheel onto the front, and may produce a more pulsing power stroke unless you have pretty good technique. --203.59.191.106 (05:09, 2 March 2007)

 * While the study did not find a difference in "efficiency", it did report that "heart rate was about 8 bpm higher when standing compared to seated uphill. Ventilation was also higher." "Standing is a bigger stress on our aerobic and cardiovascular system." Not a good idea if one is already close to their maximum exersion level. Standing and trying to maintain the same pace can lead quickly to going anaerobic. -AndrewDressel 19:02, 2 March 2007 (UTC)

 * Yes, higher heart rate, higher ventilation. (Advisable - who's to say? Riding out of the saddle is a little to common to say its in advisable.) So what we have is actual higher power output, that can take you anerobic quite quickly. Just the thing for getting over a hill and having the recovery over the other side. Nothing unusual there, and very much shows why bents are seen as poor performers on hills. You can't get out of the saddle to develop a short period of very high power, anerobically.

There is a lot of nonsense going about on 'pushing harder against the seat back' than is possible when 'pushing against gravity'. At a 60 or higher cadence, you are not going to push your weight up into the air as you pedal an upright. You will alleviate a little of the weight that is on the saddle is all. -203.59.191.106 (05:09, 2 March 2007)

 * I don't think anyone is talking about 60 rpm here. The perception is that, for very slow cadance, up a "crank stopper" for instance, one can generate more force by pushing against a seat back than by lifting ones entire body weight. Since I can press with one leg at the gym more than my total body weight, I'd have to agree with this perception, although I have to admit that it is less efficient due to energy lost in the compression of not-perfectly-elastic seat and flesh. -AndrewDressel 19:02, 2 March 2007 (UTC)

 * If we are talking about getting up a hill, then we must be talking about higher performance, so we must be talking about at least 60rpm. I thought 60 was pretty low, if you are tackling a hill. If you have a 'crank stopper' you obviously don't have the appropriate gearing, and the experience is usually as you come to a stop, defeated by the hill. Yes, you can generate more force at this low crank rate than on an upright, but that is a disfunctional technique, damaging knees, lower efficiency. I don't think this riding mode should be presented as something that recumbent cycling gives you. Is there any advice anywhere that actually says not to 'spin'? is there any experienced rider that would advocate this? Pretty clearly not.

Witness the lack of verticle movement as a road bike rider passes by. Standing up on the pedals does not alter the gravity effect, but allows you to pass some of the pushing effort from the leg alone over to the rest of the body, which it does by rocking the hips slightly to aid the stoke and reduce the legnth of the stroke as experienced by the leg so the knee is less bent at the apex of each stroke and is postioned to handle the extra power.

If you see that logic, then you also understand why new bent riders struggle uphills. It also explains the trend to shorter cranks. Its because the upper body is isolated and cannot be invoked as it can on an upright bike. Bent riders compensate by spining higher (although not higher than other good riders do) and by building more leg mass.

There is a lot of talk of the extra weight of a recumbent accounting for the poorer hill performance - a factor, but not an explanation - if the model I've suggested is right. -203.59.191.106 (05:09, 2 March 2007)

 * [responding to the para below]'Motionless in the context of not going up and down' and 'isolated from the pedalling activity' are not the same thing. Imagine you are at the finishing line watching a UCI road bike race as the leaders sprint towards you ... now, what movement do you see? You see sideways swinging of the frame, because they are effectively using it to lever the pedal against the foot with each stroke, applying the whole body to the task of generating maximum power. I'm tempted to suggest that no rider can generate more power on a recumbent than they could on an upright. (OFFTOPIC: While many recumbent enthusiasts bemoan the UCI ruling to exlude bents from those races, if you observe the quite different scope for riding technique and the importance of that and aerodynamics and teamwork to the natuer of the cycling sport, you can see that it may have been a decision to preserve the nature of the contest, rather than a spiteful 'I don't want to compete against recumbents' decision.) —The preceding unsigned comment was added by 203.59.185.129 (talk) 01:34, 3 March 2007 (UTC).

 * I don't understand your last point. First you mention the motionless upper body of efficient seated hill climbers, and then you seem to attribute poor recumbent climbing performance to an isolated upper body. Extra weight seems a lot easier to believe. -AndrewDressel 19:02, 2 March 2007 (UTC)

 * 'Motionless in the context of not going up and down' and 'isolated from the pedalling activity' are not the same thing. Imagine you are at the finishing line watching a UCI road bike race as the leaders sprint towards you ... now, what movement do you see? You see sideways swinging of the frame, because they are effectively using it to lever the pedal against the foot with each stroke, applying the whole body to the task of generating maximum power. I'm tempted to suggest that no rider can generate more power on a recumbent than they could on an upright. (OFFTOPIC: While many recumbent enthusiasts bemoan the UCI ruling to exlude bents from those races, if you observe the quite different scope for riding technique and the importance of that and aerodynamics and teamwork to the natuer of the cycling sport, you can see that it may have been a decision to preserve the nature of the contest, rather than a spiteful 'I don't want to compete against recumbents' decision.)

I have another problem with this part: "On an upright bike, the maximum force a rider can exert on a pedal is a function of their own body weight and how hard they can pull up on the handlebars." In the clipless pedal age, this is irrelevant. Pushing the pedal is not the only means of turning the cranks, it's also possible to pull the pedal on the upstroke, and this applies to recumbents as much as uprights. Also, swinging the frame from one side to another is another means by which upright riders can invoke extra muscle groups to transmit more power. Recumbent riders, by pushing back against the seat, are surely doing the same thing by invoking the muscle groups in their back? --Eamonnca1 23:55, 28 August 2007 (UTC)

Safety of Recumbents in MVAs
I would think that this wiki page would be better served by discussing the safety implications of being involved in an automobile accident in a recumbent. While it's important to promote the pros of riding recumbent, it's a disservice to readers to not openly discuss the cons.

When a car hits an upright bicycle, generally the impact will be at the riders lower leg level, 2-3 feet below the riders centre of gravity. This will likely throw the rider up and over the vehicle. However on a recumbent bike, the impact will be at the riders legs, hip, and torso, directly at the centre of gravity. This will cause the rider to absorb more of the impact energy and there is a greater chance of being run over by the vehicle.

Further, it's a valid point to recognize that, with the head closer to the ground, there is less visibility over cars, bushes, newspaper boxes at intersections, etc... Temple 21:36, 2 February 2006 (UTC)

 * That is entirely speculative. I know of absolutely no credible data to support the suggestion that a 'bent rider is likely to come off worse in a car v bike collision - and one of the common causes of fatal collision is a car pulling out into the path of the bike; in these circumstances hitting feet-first is likely to be a great advantage.  No two collisions are the same.  I have no idea how comon car v 'bent collisions are, they seem to be very uncommon indeed even given how rare the bikes are (I only know a few dozen recumbent riders personally), but that may be because the kinds of riders who ride 'bents have some idea how to ride properly so they don't get hit in the first place (and they are less likely to ride on footways, which is very dangerous).  I think it's almost certainly the case that recumbent safety is neither better nor worse than for "wedgies", but that there are slightly different issues. - Just zis Guy, you know? [T]/[C] [[Image:Flag of the United Kingdom.svg|25px|  ]] 22:39, 2 February 2006 (UTC)
 * So why are only half of these issues mentioned in the article? —The preceding unsigned comment was added by 81.235.136.245 (talk) 01:29, 24 February 2007 (UTC).

I know of two stories reported to me where people have come off their recumbent. Each one was fearful of how much worse they'd have been if they had been on an upright bike. But this is an encyclopedia, it does not contain stories.

Userbox
If you like userboxes (userboxen?), you can give recumbent riding some loooove with this one: Template:User bentcycling. - FlyingOrca 14:43, 23 April 2006 (UTC)

# 2.2 Healthy
Pardon me if I am dearly wrong but shouldn't that read 2.2 Health

POV
The article seems very much like it was written from an apologetic standpoint in favor or recumbent bicycling--it refers to upright bicycles as wedgies instead of their traditional name, and in the disadvantage section even tries to explain away at least one quantitative disadvantage (price). There are also several non-encyclopedic phrases, especially the things that appear in parantheses "(Test ride... test ride... test ride...)" -Mance 21:57, 30 June 2006 (UTC)

 * Well, it's true that bent riders do tend to be an enthusiastic lot... but I think without exception they would say that is because recumbents really ARE superior. Be that as it may, it wouldn't hurt to tone down some phrases. The "wedgie" thing is worthy of inclusion, being quite widespread, but perhaps it should be presented in another fashion? (e.g. Recumbent riders commonly refer to upright bikes as "wedgies" due to the percieved comfort advantages of recumbents and to the perceived comfort and health disadvantages of uprights, such as neck strain and penile numbness.) As for the "Test ride" thing, I agree that it's non-encyclopedic. Care to take a stab at some edits? - FlyingOrca 00:43, 1 July 2006 (UTC)

 * Biggest problems I see really come down in the Advantages/Disadvantages, which basically seems to be saying that there are many ("too many to list") advantages to a recumbent bicycle over an upright bicycle and that all of the perceived disadvantages aren't disadvantages at all, just misconceptions. Did a rewording and reformatting, but I attempted to keep all factual and NPOV content. Lemme know what you think. -Mance 05:34, 1 July 2006 (UTC)

 * I'm liking it so far. I'd do some work in this myself today, but I have a client breathing down my neck for some paying work. ;-) FWIW, the health and comfort benefits are probably the most important to recumbent riders, and are often the reason people get their first recumbent; I'd strongly suggest their inclusion in some form. Cheers! - FlyingOrca 11:53, 1 July 2006 (UTC)

 * Oh, they'll definitely be in there--it's just that the hour was waxing late, so I needed to break it off and get some sleep. I -am- going to tag all of it with needs citation--getting a few scientific (or otherwise) sources in there will significantly reduce the fanboy feeling it gives off now.-Mance 15:17, 1 July 2006 (UTC)

I have made some contributions to the existing injuy sections of the page. I noticed that mention of the "leg-suck" roll-over injury had been removed. I have reinserted it but freely admit that there may be no citable source for information about this type of injury. At most I can vouch as a participant on several recumbent discussion groups, that leg-suck is one of the most often described injury types effecting novice and experienced bent riders alike. The spiral femur fracture injury class which stood unchallenged in the article is much less common. Ironically, I have direct (unverifiable I know) knowledge of at least three cases of this devastating injury. While I am myself a bent fan, I would appreciate it if we could find a way to keep these safety warnings in the article while somehow meeting Wikipedia's verifyability standards. Both injury types come up in periodic discussions on the widely respected Bent Rider Online message forums.--RZech 17:57, 6 July 2006 (UTC)

Inability to "bunny hop"
Are recumbent bikes more difficult to ride over obstacles? On an upright bike you can lift the front wheel over obstacles and redistribute weight for the back wheel, or if you want to clear an obstacle at speed just bunny hop straight over it. I ride a lot around the city I live in and find I am always going up curbs, over ditches, over medium strips etc. Riding a recumbent bike would be very inconvenient for me.
 * That's a good point. Anyone want to weigh in?-Mance 09:14, 6 July 2006 (UTC)
 * It's true. It's very hard to unweight either end on a recumbent.
 * I say, use the right tool for the job. Urban commuting probably does not benefit from a recumbent, but a mountain bike would be useful.  A longer ride benefits from the comfort of a recumbent. Walt 11:43, 6 July 2006 (UTC)

 * I used one every day for some years as my commuter bike, first on a 15 mile round trip then on two short trips with a trian journey in the middle. I now have a Brompton which is more convenient on the train, but the 'bent was fine in every other respect. No, you can't bunny-hop. I can't do that on a wedgie either. Or on the Brom, for obvious reasons. I don't think it's especially relevant.  Just zis Guy you know? 12:00, 6 July 2006 (UTC)
 * Well, it is sorta relevant, because it widens the gap between the recumbent as a recreation vehicle with the upright as a utility vehicle.-Mance 17:08, 6 July 2006 (UTC)

 * Not really, I know plenty of regular recumbent commuters. Guy 17:33, 23 October 2006 (UTC)

Those darn Humans: --RZech 18:22, 6 July 2006 (UTC)

 * Jim Parker "weighing in" on the "unweighting" issue... There are many recumbent configurations and I am not familiar with all of them.  However I am very familiar with the Cruzbike, which is a SWB PBFWD recumbent with dual suspension. At slow speeds, the bike can be ridden up full-size city curbs.  I believe having the front wheel under power allows it to "lift" the front end of the bike over the curb, rather than just slamming into the curb as a rear-drive recumbent would do. At higher speeds, the bike can be easily lifted in a fluid motion over the curb.  I demonstrate these techniques on video Cruzbike curb climbing [User:jp308| Jim Parker] 21 January 2007

I believe that the persons with the most knowledge in riding in urban environments would be messengers.... perhaps we could get one to comment on what bike is most appropriate for the urban riding, as they seem to do more riding in the major cities than anyone else.

ROBO
 * It is not possible to bunny hop a recumbent. This may or may not be an issue for a cyclist.  This is precisely what makes recumbent bicycles useless on technical singletrack (and I'd argue the need for suspension aside from the tires, but that is subjective... if you don't need the ability to bunny hop, j-hop, or wheelie a bike the trail you are riding probably doesn't need suspension).  In an urban situation this may be a problem: per the messenger comment, no sane messenger would ride a recumbent.  You often have to bunny hop curbs, manholes, and need to be visible to other vehicles not too mention easy ingress/egress.  FWIW, I've never seen a recumbent in an actual urban environment off of a bike path.  — Preceding unsigned comment added by Ezweave80 (talk • contribs) 22:11, 26 September 2011 (UTC)  Ezweave80 (talk) 22:15, 26 September 2011 (UTC)
 * OK, weighing in on this long-dormant discussion. Back in the day I was a bike messenger in Boston.  I did not bunny hop up or down curbs (hey, I was a roadie back then who had never experienced the joy of technical off-road riding at that point).  Still, there is NO WAY I would ever be a bike messenger on a recumbent.  I have two of them, and I love them dearly, but for messenger work, you need to be "up there" so you can see and be seen.  Plus, an upright bike is just more nimble and responsive, at least in my subjective view.  Still, I'd messenger on a bakfiets without hesitation, because I would be up high enough to feel "in control" of the situation.  Ebikeguy (talk) 22:37, 26 September 2011 (UTC)

 * If I had a choice, I would ride an upright in an urban setting. I have, however, ridden my loaded touring recumbent on city streets through several cities without hesitation when they happened to be on my route. It would be a lot of extra miles to go around all of them on the way from Connecticut to Kitty Hawk. Bunny hopping is handy, but it is not necessary for urban riding. If it were, probably 80% of the riders in New York City would be eliminated. I don't know how to bunny hop my recumbent, but I would not be surprised to learn that someone has figured out a way. -AndrewDressel (talk) 23:22, 26 September 2011 (UTC)

Unsourced
I removed an anonymous addition: "Recumbents are also harder for motorists to spot, making accidental collisions more likely; for this reason many recreational recumbents sport an easily-seen banner on a pole attached to the back (though this increases air resistance)."

This is unsourced. I know of no research basis for this, anecdotal evidence suggests that recumbents are sufficiently unusual that they get noticed very easily (the "wtf? factor"). That siad, as this is WP:OR I think we wait for a credible source first. Just zis Guy you know? 15:52, 7 July 2006 (UTC)

A researcher in the UK found that traffic gave him a wider berth when he dressed as a woman wearing a wig. That study may supports the claim that the way you look influences how traffic in general flows around you. There is no doubt that in the mind of the general public, nearly everyone I meet says this to me "those low bikes look dangerous, someone might not notice you". I think its fair to mention that many people think this, it may be true but there is no clear study either way. Being so low does seem to result in accidents, at least its not hard to find someone report they were hit on the trike by someone who didn't see them. Also not mentioned is the difficulty of riding defensively if you have less information about where the traffic is moving.

 * If there isn't a study or similar citation showing that recumbents are more likely to be involved in an accident, it should not be included in the article. Just because it may "seem like that" to a lot of people is not a justifiable reason for including it.  The counter arguments that recumbents are MORE visual hold just as much weight.  No citation, no inclusion IMO.  Same thing regarding the riding defensively comment.  Most recumbent riders, and indeed most upright riders (especially roadies) who have tried a recumbent, note that the natural position puts you in a position to naturally view the world around you.  This is opposite of a road bike, which naturally puts you in a position of looking at the road beneath you.  Again, no citation, no inclusion.  IMHO though, a recumbent puts you in a position to monitor traffic in front and to the side of you much easier, while making it naturally harder to check behind you without the aid of mirrors.  Saberswordsmen1 (talk) 11:38, 14 October 2009 (UTC)

There has to be some research that says as much. Common sense dictates it. I don't know about your locale, but in the major cities I've lived in (and in the city, not the suburbs) you will never see recumbents in bike lanes or in city traffic. Ezweave80 (talk) 22:21, 26 September 2011 (UTC)

Even though this is as unsupported as everything else, I have to chip in. Most recumbents are as high as or higher than children's bikes and this particular criticism is rarely made with children's bikes. I ride a low rider which indeed is quite low commuting 35km each way; I have never been overlooked. Still, this is anecdotal. Thniels (talk) 13:58, 10 October 2011 (UTC)

Unsourced claims in Advantages section
"Handling. Because of its low center-of-gravity, the recumbent bicycle can handle sharper turns at greater speeds than a traditional upright bicycle."

 * Any idea how this might be true? If the same physics apply, then a recumbent will need exactly the same lean angle as an upright bike to make the same radius turn at the same speed. True, the combined center of mass of the bike and rider will be displaced from the vertical less, but that doesn't necessarily give it an advantage. The only limiting factors for both types of bikes should be friction of the tires on the pavement, interferance from other parts of the bike touching the ground (pedals or seats), and the riders nerve. -AndrewDressel 04:25, 3 August 2006 (UTC)

Having a low CoG means you can change direction faster, because the mass has a lesser distance to move for a given amount of lean, but also adjustments will be less fine (all things being equal which they never are).

 * I can't corner at 50 on a wedgie... Guy 17:32, 23 October 2006 (UTC)

"Stability. Because of a lower center of gravity and a more aerodynamic design, recumbent bicycles enjoy greater stability than traditional upright bicycles. In addition, panniers can be mounted low, under the rider, which gives good handling and stability when loaded."

 * How does a lower center of gravity make recumbents more stable? In fact, J. Fajans claims the opposite, as do Whitt and Wilson on page 232 of Bicycling Science. Even the first advantage listed in the section immediately following contradicts this. -AndrewDressel 04:25, 3 August 2006 (UTC)

 * Agreed. But lowering the CoG seems to offset the problems with the pendulum effect.  Low riders improve ride in a way that high loading does not, don't ask me why. Guy 17:32, 23 October 2006 (UTC)

A longer wheel base brings stability, in that steering corrections more slowly alter that balance. Low racers have longer wheelbases than normal bikes. Bill Patterson's book Lord of the Chainring may be helpful resource. In fact, he might be enticed to help here. Is there a bicycle handling wiki page yet? -124.168.109.248 05:29, 5 March 2007

 * The attribute of "more slowly" altering balance can also be seen as destabilizing in that more steering input is required to maintain balance. The closest things to a handling wiki page so far is either Bicycle and motorcycle dynamics, Bicycle and motorcycle geometry, or Bicycle frame. -AndrewDressel 15:00, 5 March 2007 (UTC)

Advantages and disadvantages of recumbent riding position
The current article mentions All unsourced, of course, and to which I would add: On the other hand here are some citable points: Anyone else have any data points that can be referenced? -AndrewDressel 17:46, 6 December 2006 (UTC)
 * [The recumbent position] reduces the rider's hydrostatic pressure, thus allowing venous blood to more easily return to the heart. This physiological effect of improved circulation suggests an increase in rider endurance and/or increased power output on long rides.
 * the [recumbent] rider is unable to stand on ascents
 * the [recumbent] rider can push against the seat to generate more pedal force than is possible on an upright bike because on an upright, the rider cannot press a pedal downward with any more force than his own weight
 * recumbents have won hill-climb challenges and races with substantial ascents against uprights in mixed fields, and have been ridden over the mountain stage routes of the Tour de France.
 * While pressing against the seat back may allow for more force, it comes at the cost of losses due to compressing imperfectly elastic material: muscle and other tissue of the back and foam or plastics in the seat. Any energy spent raising the CG of the rider against gravity may be recovered.
 * A study by Bussolari and Nadel (1989) led them to pick a recumbent riding position for the Daedalus flight even though the first English Channel crossing was accomplished with an upright position. This is according to Wilson in his third edition of "Bicycling Science" on page 72.
 * He continues on page 86 to cite Drela (1998) who "confirmed that there was no significant difference in power output between recumbent and conventional bicycling."

land speed record link needed
The opening paragraph mentions the land speed record for human powered vehicle, but no link or citation is given. There seems to be no pae for it on Wikipedia. stib 02:31, 6 May 2007 (UTC)

Pedal force and seat backs
Several editors have added the claim recently that recumbent riders can generate more pedal force by pushing against the seat back than upright riders. While this may sound obviously true (This doesn't need a citation. It's just simple physics. When you push against something, it pushes back.), reality is far more complicated, and this claim definitely needs a reference.

This is especially so since the one reference already cited in the Riding position section confirmed "that there was no significant difference in power output between recumbent and conventional bicycling." (Drela, 1998)

Reasons why this claim may be false or irrelevant include, but are not limited to:
 * No one can leg press more than their body weight with one leg more than a few times anyway.
 * No one can leg press more than their body weight with one leg at the rate necessary for efficient pedaling.
 * Energy lost through inelastic seat back compression, compared to perfectly conservative gravitation, negates any advantage that the greater force may bestow.
 * Since force = (mass x acceleration), not just weight, upright riders are not limited by their body weight when generating pedal forces.
 * Etc.
 * Not sure I agree with any of this. Point 1 - 1-legged jump-roping is applying more force than your body weight, Point 2 - people standing on their pedals tend to pedal much slower than sitting, 3 - say back compression is 90% efficient, if you're applying 2x the force that's still significantly more power than gravity, 4 - acceleration in this case for an upright is capped at <1G without hopping out of your pedals, unless you're pulling down with your arms. I think the real matter is more of being able to switch back and forth from standing on the pedals to spinning in a lower gear, to activate different muscles.  In a recumbent, there is less switching of riding styles so muscle fatigue is a bigger factor. Nerfer (talk) 15:44, 15 September 2016 (UTC)

Even recumbent competitors tend towards the extreme supine position, presumably giving up whatever advantage they could have from pressing against their seat back in favor of better aerodynamics. -AndrewDressel 17:31, 24 May 2007 (UTC)
 * An upright bike allows the use of the arm muscles to generate extra force by swinging the bike against the pedal stroke. A recumbent does not allow this. --Eamonnca1 (talk) 18:31, 10 January 2008 (UTC)
 * Except the Cruzbike (any pivoting-boom recumbent, of which Cruzbike is the only current manufacturer, AFAIK). You can pull on the handlebars to swing the pedal toward the pushing leg, much like someone standing on the pedals will swing the bike back and forth. I don't know of any scientific analysis of that, so I'm not going to put it in the article, but they do claim the Cruzbike climbs better than other recumbents (similar to uprights) for this reason. Nerfer (talk) 15:44, 15 September 2016 (UTC)

Removal of Section "Other" under "Disadvantages"
I've deleted the entire section "Other" because: --Theosch 19:28, 6 June 2007 (UTC)
 * The first sentence (higher rolling resistance of small wheels) is only true in some cases and in any case not a special characteristic of all recumbents.
 * The second sentence about heel overlap is a valid point which I moved (shortened) to "Disadvantages".
 * The third sentence about possible injuries is too long and doesn't really belong here.

I've replaced the section regarding unique recumbent injuries as they are a discriptive part of the recumbent experience. I'm not certain what "too long" of a sentence is. Also reinstated is the section describing the debate about the use of clipless pedals on recumbents. Their widespread use among avid upright bicycle enthusiasts does not automatically transalte to the recumbent. Some mention of this difference seems instructional and appropriate. Raz711 21:38, 19 July 2007 (UTC)

USS picture
There isn't any. I hope a clear picture can be provided of the Steering Under Seat arrangement. Jim.henderson (talk) 19:33, 22 January 2008 (UTC)

 * Done. Hope it is clear enough. -AndrewDressel (talk) 20:27, 22 January 2008 (UTC)

Incomplete part about safety
"Safety A type of injury characteristic of recumbents called "leg suck" occurs when a foot touches the ground and the bike runs forward over the contact point, causing ligament damage and in some cases ankle fractures. The use of clipless pedal reduces this possibility by preventing the foot from slipping off of the pedal. But with clipless pedals, remaining clipped in during a front tire or wheel failure at high speeds can result in the recumbent rolling over the rider and taking a clipped in leg or legs with it. This scenario, although very rare, can create severe spiral fractures of the femur rarely seen with upright bicycles. Except for these injury classes, recumbents are generally considered safer than upright bicycles. Many upright bicycle accidents involve the rider going over the handlebars with resultant head injuries. Recumbent riders are less prone to these types of injuries."

There are systems which keep the feet in place on the pedals but also have a mechanism by which you can easily detach the feet if necessary. You can adjust the strength which is needed to relaese your feet and your feet will only detach from the pedals when you put the force in specific directions (to the side). So, as long as you are normally cycling the feet will stay on these pedals, when you have an accident then the feet will be released from the pedals.

Another big advantage is that you can generate a higher speed when you can also pull the pedal up in stead of only pushing the pedal down (racing bike vs. ordinary bike). Pieter pietersen (talk) 00:24, 25 April 2008 (UTC)

Highracers
"Many newcomers to recumbents find that high racers are the most difficult recumbent to ride initially, due to the rider's stationary and high center of gravity and the bike's short wheelbase."

 * 1) Center of gravity height is already discussed in the Disadvantages section. There a higher center of gravity is said to be easier.
 * 2) With respect to what is the rider's center of gravity "stationary"? The bike? Wouldn't that be true for all recumbents?

 * -AndrewDressel (talk) 14:37, 3 July 2008 (UTC)

 * I agree the phrase could be clearer. I see it has already been removed. Here are my thoughts:

 * (1) The higher center of gravity is, in fact, easier to balance ONLY IF you can move your upper body in order to achieve that balance. This is generally not case with recumbents.
 * (2) I meant "stationary" to refer to the fact that the upper body is in a fixed position in the seat, not readily capable of being moved side to side on the seat for purposes of balance -- unlike on a road or mountain bike.

 * In general, I think newbies to 'bent riding should know that high racers are harder to balance. Many folks besides myself have found this to be true. I tried to summarize why this is so, but perhaps I was brief to the point of obfuscation.

 * I'd like to re-add the statement, "Many newcomers to recumbents find that high racers are the most difficult recumbent to ride initially," if there are no objections.

BikeZen.org (talk) 00:31, 6 July 2008 (UTC)

Seating position nonsense
"Constant position. While the riding position is comfortable and removes stress from the arms, it cannot easily be varied during a ride (as upright riders might stand for a hill)"

I rode my recumbent today, and I can shift around in the seat just fine. You put your weight on the pedals and your shoulders, and then shift your butt to where you want it. You can skooch around the seat no problem. 89.240.148.165 (talk) 22:56, 3 July 2008 (UTC)

There are reasons to adjust position, but at least some of them aren't going apply as much on a recument, if at all. Tired wrists wouldn't apply as much since much less pressure is applied (arms generally are weight bearing on recumbent). Sore sit bones are unlikely to occur due to different mechanics of the seat. Saddle chafe is unlikely to occur, again because of mechanics of the seat. Tired back is also less likely to occur since it is generally in a relaxed position on a recumbent. So why is this even a disadvantage if the reasons prompting a change in position aren't even valid on a recumbent? —Preceding unsigned comment added by 67.52.139.34 (talk) 08:38, 3 May 2010 (UTC)

Safety
"Safety. Particularly with the lower designs, the recumbent bicycle's low center-of-gravity and short distance from the ground significantly reduce the consequences of a fall for the rider. It is also possible to cycle very close to the curb without risking a pedal-curb collision. A fall from a recumbent may be less harmful than from an upright bike due to the feet-first orientation ensuring that the rider never goes over the handlebars. The low center of gravity greatly increases braking and stopping capabilities."

1. While it can be argued that the energy at impact due solely to the fall will be less for a bike with a low CM, it says nothing about the orientation of the body upon impact and the damage done due to the impact at that orientation or the subsequent skid along the pavement at that orientation. Without an appropriate reference, which is currently lacking, this article cannot state anything about the consequences of a fall.

2. The feet-first orientation does not ensure that the rider never goes over the handlebars. The location of the rider with respect to the front wheel is the largest factor. SWB recumbents with the front wheel behind the feet may be just as likely to perform an endo or stoppie as an upright bike.

3. The low center of gravity does not guarantee any better braking or stopping capabilities. As noted above, endos are still possible. On the other hand, LWB recombents may skid the front tire under hard braking resulting in loss of directional control and balance.

-AndrewDressel (talk) 18:12, 7 July 2008 (UTC)

 * I have some sympathy with what you are saying, but on the other hand I find the obsession on Wikipedia to cite a reference for every sentence unhelpful and something that spoils the flow of articles. For some topics a citable reference may simply not exist, even if it is a self evident or commonly understood fact (eg. within communities of interest such as forums) - and simply adding a reference to someone's Blog does little to improve the accuracy anyway.

 * That aside, with respect to the points above, a lot seems to depend on the design of the recumbent - there are so many designs that it is unlikely that a single statement can be made. If we consider a low-racer design, with 20"/20" or 20"/26" wheels and the rider positioned between the wheels then I think it is highly likely that points 1 and 2 do apply - it seems self-evident that if you fall from a  much lower distance in an already horizontal position you are, on average, less likely to be injured than if you fall from 2 or 3 times the height from a more vertical position where you are more likely to be "thrown" from the bike on collision.  Likewise, on average,  it is much harder to go over the handlebars than on an upright.  I don't think we need to find a website to cite to make that statement.  However, with other recumbent designs - high riders and LWB designs then I agree that these statements become weaker.  Regarding point 3) the US Dept of Transport survey I referenced does provide objective evidence that recumbents have better stopping capabilities than regular bikes.  However, it does not discuss the mechanism for this (ie. whether it is related to the low centre of gravity).  Having said all that, I therefore suggest that the text is reworded as follows:

 * "Safety. Particularly with the lower designs, the recumbent bicycle rider's short distance from the ground and horizontal posture will generally reduce the consequences of a fall for the rider. The fall  may also be less harmful than from an upright bike due to the feet-first orientation, ensuring that it is less likely that the rider goes over the handlebars.  Recumbent bikes have been shown in independent studies to have much shorter stopping distances, although the mechanisms for this have not been analysed.  The high pedal position also allows riders to be closer to the curb without collision."

 * In my extensive experience of falling off both upright and recumbent bicycles, the anecdotal evidence suggests that you're more likely to slide down the road, with accompanying skin loss to arse and elbows, on a recumbent. Mr Larrington (talk) 13:33, 1 July 2009 (UTC)

 * Paul (talk) 05:38, 8 July 2008 (UTC)

This is what Sheldon Brown had to say about recumbent safety: "Crash-worthiness

 * Most bicycle accidents do not involve other vehicles. (If you are going to crash on a bike, a recumbent is the best way to go.)

 * If you crash head-on into another vehicle or a stationary object, the feet-first position of the recumbent rider is the best possible one.

 * If you fall over sideways, you do so from a much lower height.

 * Add the recumbent's greater stopping power and you have to judge them substantially safer than upright bikes."

http://www.sheldonbrown.com/recumbents.html

Now Sheldon was "da man" so you aint allowed to argue with his opinion ;) As for a little original research, it is physically impossible for me to do an endo on my Short Wheelbase recumbent.  I can fully lock the wheels at speed, and the most that has ever happened is doing a little "stoppie" where the back wheel lifts off the ground slightly.  It is so weighted that it just falls right back down again.  78.148.165.71 (talk) 13:02, 8 July 2008 (UTC)

Version of English used
The little edit war between 75.156.75.40 and Thumperward caused me to take a look to see which version of English we should use, per ENGVAR The topic has no strong national ties to either, and the current article has The original stub used "centre", but the current Bicycle article is in American English. At this point, I'd say the article "has evolved using predominantly one variety, the whole article should conform to that variety." I suggest we alter the two British English words I can find to match the rest of the article. -AndrewDressel (talk) 15:17, 1 November 2008 (UTC)
 * 1) "centre" once and "center" multiple times.
 * 2) "fiber" is only used once and spelled the American way only.
 * 3) "tyre" once and "tire" multiple times.
 * 4) "maneuverability" as a section heading and "maneuvers" in the text.

Sheldon Schmeldon
Wow! PEHowland makes an edit based on what he freely describes as his own original research: as a recumbent owner this is definitely not the case.

He then dismisses the reference to Sheldon Brown's website, whose knowledge of bicycles The Times describes as encyclopaedic and who is cited by over 40 other Wikipedia articles, as an unsubstantiated blog instead.

Well, how about this by Gretchen Konrady, Group Health staff writer at Group Health Cooperative:
 * Recumbent means reclining, and these riders are in a seat (rather than a saddle) with their legs stretched out in front. This riding position works for some cyclists seeking to avoid neck, back, and wrist pain that the upright position can cause or aggravate.

Or this by Paul K. Nolan, M.D. in Medical Benefits of Recumbent Bicycles reprinted from Recumbent Cyclist News at Cycle America:
 * The upper extremities are not forced to doing something they were not anatomically designed for. The pains in the neck, shoulders and arms of day long rides disappear.

Without any, let alone comparabale, real references to the contrary, the detail should remain. -AndrewDressel (talk) 23:32, 13 September 2009 (UTC)

 * My word, you do have an irritating and self-important attitude - is that intentional? - Paul (talk) 04:29, 14 September 2009 (UTC)

 * I hope you will excuse my reformatting of your comment slightly. I know it is frowned upon, but I feel it necessary to reply directly to your single sentence above.

 * Yes, I can imagine it is very irritating to own a recumbent that hurts your neck so much while I keep finding references that exalt the neck strain reducing properties of recumbents in general. That is not an attitude, but simply how Wikipedia works. Sadly, your personal experience matters not one bit, and I suspect that there are no references to be found to support your position, or we would be reading them here.

 * Indeed, there have been no studies on the subject of neck comfort, so neither of us have any objective evidence to provide. This is why I originally removed the claim.  All any of us have to offer is hearsay and opinion pieces.  My irritation was with the tone of your response, not my bike.  Paul (talk) 04:33, 15 September 2009 (UTC)

 * As for your accusation of self-importance, that's pretty funny. It is exactly my understanding of my lack of importance as a Wikipedia contributor that keeps me from referring to any of my own experiences. I can only imagine what led you to begin this chain of edits by invoking yours. -AndrewDressel (talk) 02:30, 15 September 2009 (UTC)

 * Very good Andrew. I note you have ignored the details of my explanation below, which have nothing to do with my own experiences.  However, I trust the way I caveated the original claim is now satisfactory to you.  By the way, have you tried my experiment at the bottom of this set of comments.  Perhaps you'll then understand why some recumbent designs are not comfortable on the neck... Paul (talk) 04:33, 15 September 2009 (UTC)

 * At least you now provide references (although none actually refer to any scientific or statistical study on the matter and so remain no more than opinion pieces) and I will let the edit stand to avoid an edit war. I note Nolan's article was published in "Recumbent Cycle News" (hardy likely to publish a critical article) not any medical journal and is based on his casual observations of some cyclists when out cycling (hardly a rigorous medical study) and Konrad's article is equally anecdotal based on a sample of one person. I see that Sheldon Brown carefully caveats his claims of comfort with "are generally more comfortable" but provides no source for even this caveated claim.

 * The very fact that many recumbent manufacturers offer head rests for their bikes seems evidence in itself that there is an issue with support of the head. Likewise just look at any image of a rider on a recumbent (particularly on short-wheelbase low racers) and you will see that the head is held in a totally unnatural position (look at Mr Brown himself to see what I mean).  Finally, the fact I do get neck ache when riding my recumbent (and never on a traditional bike) clearly indicates to me that not all recumbents remove neck pain - mine causes it!  A casual Google of a popular recumbent chat forum reveals others with similar stories.

 * HOWEVER, note, I did not put "neck ache" as a disadvantage (then I would have been adding material to the article based on no citations). I simply removed the claim and let it remain unmentioned.  This is very different.

 * Nevertheless, I feel the claim is dishonest and the whole section on advantages/disadvantages reads like a schoolyard pissing contest on recumbents rather than an entry in an encyclopedia. Note, I can understand that owners of more upright recumbents (particularly the long-wheelbase designs more fashionable in the US) would not have neck discomfort and perhaps this is where the confusion lies.  It's obviously a function of how horizontal the riding position is.  Without more discussion of the actual riding position, any article discussing comfort or otherwise of neck pain is somewhat meaningless.

 * On reflection, I have modified the article to say "Depending on the wheelbase and the seat angle, ...". Hopefully this is a reasonable compromise and more objective statement of reality.

 * Paul (talk) 04:29, 14 September 2009 (UTC)

 * Sounds like a good compromise--better than a compromise really. My only concern is "depending on wheelbase"...why would it depend on wheelbase, except insofar as wheelbase affects seat angle, in which case that is covered by "depending on seat angle"? --Ccrrccrr (talk) 05:35, 14 September 2009 (UTC)
 * I guess it only depends on wheelbase in the sense that riders on long wheelbase bikes tend to be sitting in a more upright position (almost like sitting in an armchair) than on a SWB where the legs (and by extension, the back) tend to be much more horizontal. Happy for the wording to be modified though, the real point is that there is such a range of recumbent designs that I don't think it is possible to make a single claim.  In general, this a problem with the whole advantages/disadvantages section - any particular design will probably have some of the advantages and some of the disadvantages, but none will have all of each, as the design is a normal engineering compromise. Paul (talk) 05:50, 14 September 2009 (UTC)
 * One further thought on this issue, and particularly Andrew's quote:

 * The upper extremities are not forced to doing something they were not anatomically designed for. The pains in the neck, shoulders and arms of day long rides disappear.

 * I offer this simple experiment to illustrate why the above statement is incorrect for some recumbent designs. In the typical highly reclined short-wheel base design, the rider is almost horizontal.  So, try this simple experiment: lie down flat on your back on the floor, and then lift your head up so that you can see your toes clearly.  Hold that position for a couple of minutes.  Now, does this feel natural and does your neck ache?  Duh. Of course, this position is exaggerated compared with the recumbent, but it illustrates the point - and on the bike you are holding your neck in this position for perhaps an hour or two, not a couple of minutes.  Obviously, the closer you angle your back to the vertical, the less your neck has to crane forward and the more natural the position.  Hence the dependence on bike design and seating angle.  Paul (talk) 08:48, 14 September 2009 (UTC)

Framing as debate
I don't like the "advocates claims"/"critics counter" wording. Neither are really the best people to listen to. Best to listen are those who acknowledge that there are both advantages and disadvantages, and that both types are useful for different purposes and different people. And that different recumbent designs have different sets of advantages and disadvantages.

I guess it depends somewhat on whether the list of advantages is a complete list of anything people say, factual or false, or whether it's a list of verifiable facts. It seems like we should have the latter, in which case we don't need the "advocates/critics" in the intros of those sections. Ccrrccrr (talk) 14:55, 15 September 2009 (UTC)
 * As I made this edit, I'll make the first comment. As currently written, the Advantages and Disadvantages section does not read like a work of reference.  It's a list of every possible idea fans of recumbents can think of, countered by every possible reason against them that critics can come back with.  In some places it has annoying "on the one hand x, but on the other hand y" type statements that simply reflect people modifying claims they disagree with with opposing points.  In all, it is not very convincing, and poorly written.  It could do with a total rewrite.  I would be happy if the section could be tidied up to read more objectively and to focus on real advantages and disadvantages rather than every minor thought.  However, other issues to be addressed are that, with a few exceptions, there is little objective evidence of any of these claims (i.e. independent statistical analysis or studies) but much reiteration of group think and references to secondary sources of information.  These may or may not be true, but are not proven facts in any scientific sense of the word.  (And I suspect in most cases, no studies have been done).  This inevitably leads to text littered with "citation" requests.  My preference was to simply acknowledge this problem by framing the section as the pros and cons cited by advocates and critics, and the issue of objective evidence goes away.  Another issue is that the term recumbent covers a wider variety of bike designs, none of which have all the advantages or all the disadvantages, and this is not addressed. Paul (talk) 17:46, 15 September 2009 (UTC)

 * Agreed, mostly. So let's consider it a temporary, non-ideal fix.

 * Where I don't agree is on "scientific" being the standard of evidence to aim for. The scope of Wikipedia extends well beyond science.Ccrrccrr (talk) 05:12, 16 September 2009 (UTC)
 * I use the term scientific loosely. Objective is the main point - whether that is scientific, statistical, legal or any other standard for objective evidence. However, a claim should reference some form of independent study, based on a statistically relevant sample size when appropriate. Otherwise the claims are subjective (and may or may not be true).Paul (talk) 09:50, 16 September 2009 (UTC)

 * That sounds reasonable, but it's not the policy of Wikipedia. One place to read about those sorts of ideas in Wikipedia is the essay WP:Truth.  If you think Wikipedia should have a different policy, that might be a good idea, but this is not the place to argue for that change.  Ccrrccrr (talk) 13:02, 16 September 2009 (UTC)
 * Fair enough. I guess it then all stems on whether the article here uses reliable sources.  From a quick read of how this is defined, it seems that this covers most of my concerns anyway.  If all the Advantages and Disadvantages could be linked to reliable sources I'd be content. Paul (talk) 16:02, 16 September 2009 (UTC)

Rear wheel steering
"A few recumbent bicycles use rear wheel steering, but these are typically less stable."

 * While I would normally wait for a reference to be provided, this claim is so extrodinary that it should wait here until a reference can be found. There are several good sources in the bicycle and motorcycle dynamics article that assert a rear wheel steered bike is unridable, except for one particular example: hardly "a few recumbent bicycles". -AndrewDressel (talk) 23:13, 4 May 2010 (UTC)

 * It's trivial to find links to these via google. There's even videos on youtube. There's nothing impossible about rear wheel steering; even land speed record cars have used rear wheel steering. The main trick seems to be to use a relatively long caster on the steering. They're clearly something you can ride.- Wolfkeeper  23:26, 4 May 2010 (UTC)

 * As you are making the claim, perhaps you will be kind enough to provide some of these links. All the ones I find either confirm that they are unridable, or actually have center steering (the Python Lowracer and Flevobike, for example). Rear-steering in three- and four-wheeled vehicles, such as land speed record cars, really has nothing to do with bicycles. -AndrewDressel (talk) 00:05, 5 May 2010 (UTC)

Half inch trail steering geometry
Half inch trail steering geometry should be mentioned. -65.101.129.33 (talk) 18:57, 26 June 2010 (UTC)

 * No sweat. Provide a reliable source, and we'll get it right in. -AndrewDressel (talk) 19:25, 26 June 2010 (UTC)

Starting a bicycle
re: disadvantges, starting and stopping in July 8 version. The article states "However, since starting a bicycle by pushing the feet against the ground is probably a poor way to start,[23] this criticism may invalidate itself.[citation needed]"  but the cited reference does not support the statement. the reference instead says that pushing off with one foot on a low pedal is a poor way to start. The embedded video at the reference shows the correct way to start as pushing off with one foot on a higher pedal. I'm changing the sentence to agree with the citation. — Preceding unsigned comment added by 199.129.149.223 (talk) 23:02, 8 July 2011 (UTC)

Quote from current text: "The recommended way to start an upright bicycle is by pushing off with one foot on the ground, and one foot on a high pedal. (...) Recumbents cannot be started with this recommended upright bicycle technique." What? This is exactly how I start on recumbents. Other ways are quite hard. For example, the "shuffle-start" technique which many use on uprights, is difficult or impossible on recumbents. Please explain better what is meant, or edit to improve. Gunnstein (talk) 11:12, 3 July 2014 (UTC)

Contribution from Spotbiker
This appears to be describing some kind of steering mechanism, but it is not very clear and completely unreferenced, so I've moved it here. -AndrewDressel (talk) 19:09, 31 May 2013 (UTC)
 * The new design of the rake tube at above the front fork of the recumbent bike will require at best performance technically call for above-seat tiller steering handlebar and its handlebar stem to connect to the 2 retainer bearings and direct fix to the twice bigger gear that is intermesh to the smaller pinion gear inside the front frame. The pinion gear steers the front fork that two fork tubes connects to the front axle wheel. By a way, the pinion gear have third and fourth retainer set of two bearings. It is called under-steering as it causes the front of front wheel to turn at near twice farther (approximately two inches) at same time the handlebar turns to a one inch in the curve's arc in the recumbent bike. That design is greatest improved in both overall: the performance and reliable of luxury at ease of use. So the Under-Steering OSS tiller handlebar system of gears is model named demeander bicycle Brand of tubing company.
 * I have made the sketch of the OSS into much more mechanical of 2 gears for improvement of steering. -Spotbiker

Recumbents vs uprights vs uprights
In the recumbents vs uprights comparisons, this article seems biased and in addition to that only considering the uprights on wich the cyclist bends forward. The city bikes that are the standard in the netherlands, have strengths and weaknesses that are verry different than upright racing bikes. They are designed for use as transportation, not sport. Safety, comfort and manueverability are considerately better than the ones designed for high speeds. I don´t have any references, but to me it seems by far the safest option for use in traffic. Because the cyclist truly sits upright, visibility and the ability to see your surroundings is optimal. Combined with better manueverability, this greatly reduces the risk of an accident occuring in the first place. Falling head down is less likely, and its also a better position to be in when you whant to hop off your bike during an incident. In my twenty years of cycling daily through the towns and cities i lived in i have experienced some incidents, and in all of them i would have been in a worse situation if it had occured while driving recumbent. Recumbent bikes are ideal for high speed long distance travel, but not the safest. Unless you ride a nearly upright recumbent bike, wich close to a city bike with extra back support. If you want to compare things, be clear what you are comparing with what. Comparing cats and dogs changes when you include lions. — Preceding unsigned comment added by 83.117.66.29 (talk) 19:02, 19 June 2013 (UTC)

 * Some good points which I have attempted to address in the article, mostly by expanding the introductory sentence to the section. -AndrewDressel (talk) 16:40, 1 July 2013 (UTC)

 * While I might disagree on some of the safety aspects brought up by "unsigned", I do agree we're trying to compare too many things and this section has become unwieldy, in an article that is already long. In particular, there are many caveats for recumbent bikes vs. trikes, and as unsigned mentions, a mountain bike or city bike (town bike, hybrid, whatever you want to call it) will be different than a head-down position on a road bike with dropped handlebars.  Maybe this section should be converted into a table instead? Nerfer (talk) 18:45, 13 September 2016 (UTC)

Recumbent trike cornering
I have moved the following item here until it can be reliably sourced:
 * Trikes are capable of turning at high speed when leaning into the corner, producing lateral "g forces" similar to sports cars.
 * First, what is leaning into the corning? Not the subject of the sentence, unless it is a tilting trike.
 * Second, the part about g forces similar to a sports car is quite a claim and definitely needs a reliable source.
 * Third, it is pretty easy to find sources, though not necessarily the more reliable, that describe the danger of "the dreaded trike flip." For example and.
 * -AndrewDressel (talk) 20:57, 10 August 2013 (UTC)

"leaning into the corner" is exactly that: Leaning your (upper) body into the turn. A tilting trike is not required for this. Gunnstein (talk) 11:47, 17 July 2014 (UTC)
 * Okay, but speaking from experience, simply leaning your body isn't going to produce as sharp a turn as you can do on something that tilts (typically with two wheels), at least not comfortably (ie. staying in your seat). Nerfer (talk) 02:37, 25 October 2015 (UTC)
 * Sure. The body lean has to be extreme, and the seat must be low, to compete with a tilter in turns. Note that if you change the text to clarify this, it should also be clarified that a tilter doesn't experience lateral G-forces at all, from the point of view of the rider, who only feels a down force (as on a bike). Gunnstein (talk) 07:12, 25 October 2015 (UTC)

"Over Distances Recumbent bicycles outperform upright bicycles..."
The above quote is from the first sentence of the 'Performance' section. The reference provided does not support the claim. To the contrary, the reference provided suggests that it is far more common in long distance contests for upright bicycles to capture the win. That sentence needs to be changed because it is misleading. It goes toward the fairly obvious slant over most of the article towards painting recumbent bicycles as superior performance machines. The fact remains that over long distances and on courses incorporating uphill sections, recumbent bikes do not compare favorably to upright bicycles. 70.171.44.124 (talk) 09:30, 30 January 2014 (UTC)BGriffin

"...it is far more common in long distance contests for upright bicycles to capture the win" Maybe because there are a lot more upright bicycles participating? Just a guess. Anyway, the reference seems to no longer say what it did when it was added, I see nothing about recumbents there now. Gunnstein (talk) 11:55, 17 July 2014 (UTC)

"The fact remains that over long distances and on courses incorporating uphill sections, recumbent bikes do not compare favorably to upright bicycles." Citation needed, implausible claim. Maybe not for long uphills, but for long distances in general it makes sense that the ergonomics and aerodynamics favour recumbents. Gunnstein (talk) 11:55, 17 July 2014 (UTC)

 * Barbara Buatois won the Women's division of RAAM outright in 2010 riding a Performer low-racer recumbent, by almost 21 hours. Mr Larrington (talk) 21:33, 4 May 2022 (UTC)

Disadvantages: Starting
"Because of the supine position, some recumbents do not allow the rider to push forward with both feet on the ground." Who starts a bike like this, with BOTH feet on the ground? Apart from pedal-less kids running bikes, I have never seen a bike started that way. For an upright bike it would require an extremely low saddle. Seems nonsensical, should be sourced better or removed.

"The recommended way to start an upright bicycle is by pushing off with one foot on the ground, and one foot on a high pedal. (...) Recumbents cannot be started with this recommended upright bicycle technique." This is exactly how I start recumbents. I'll remove that claim if it is not explained or sourced better.

"Starting a recumbent does not require great strength; it is a matter of balance and a skill which must be learned. It is best to learn from an experienced rider, who can help with a little push at first. Several rides may suffice to become confident enough of one's starting and stopping skills before becoming ready to ride in traffic or perform uphill starts." While I agree with what is said, this defence section seems misplaced here. I suggest to remove it, to keep the whole list shorter (easier to read). Gunnstein (talk) 11:43, 17 July 2014 (UTC)

Spelling: high-racer, highracer or high racer?
I've seen high and low racers used all 3 ways in the article (and in the talk page). We should probably consolidate on one standard. It seems most of the time it is written as one un-hyphenated word, even though that is flagged by my spell-checker. Nerfer (talk) 18:02, 13 September 2016 (UTC)

Replacing adv/disadv section with a table
The advantage/disadvantage section is rather wordy and a bit redundant and full of exceptions for recumbent trikes vs bikes as well. I made a table in my sandbox that can replace all that, I kept most of the text except to make it fit better where a section was merged or separated (for instance, adv and disadv sections both have "safety" bullet points, along with other bullet points on leg suck, falling, genital-urinary issues, etc. so I distributed the safety parts to the more specific points). There were two, what I considered somewhat controversial, statements that were tagged with citation needed, I deleted them, but I did keep another citation needed sentence that I felt was worthwhile.

The result, I think is visually better, although it can be harder to edit (I had to learn how tables worked, and putting citations in it can lead to some confusion over what '|' character means what). Check it out in my sandbox and let me know what you think. If I don't hear objections, I'll move it into the article (and then probably will hear objections from people not monitoring the talk page :-) ) Nerfer (talk) 18:56, 6 October 2016 (UTC)

 * Okay, it's been nearly 3 weeks, I'm going to remove it from my sandbox now. But it's still in the history. Nerfer (talk) 16:15, 25 October 2016 (UTC)

Fed
Fed and non-fed/unfed recumbent bicycle? 176.222.44.103 (talk) 21:06, 22 November 2019 (UTC)

title: Talk:Recumbent bicycle


text:
History of Tristan da Cunha

Tristan da Cunha is part of the British overseas territory of Saint Helena, Ascension and Tristan da Cunha and has a history going back to the beginning of the 16th century. It was settled by men from military garrisons and ships, who married native women from Saint Helena and the Cape Colony. Its people are multi-racial, descended from European male founders and mixed-race (African, Asian and European) and African women founders.

Discovery
The uninhabited islands of Tristan da Cunha were first sighted in May 1506 during a voyage to India by the Portuguese admiral Tristão da Cunha, although rough seas prevented a landing. He named the main island after himself, Ilha de Tristão da Cunha, which was later anglicised to Tristan da Cunha Island. His discovery appeared on nautical maps from 1509 and on Mercator's world map of 1541. Some sources state that the Portuguese made the first landing on Tristan in 1520, when the Lás Rafael captained by Ruy Vaz Pereira called for water.

17th century
Though far west of the Cape of Good Hope, the islands were on the preferred route from Europe to the Indian Ocean in the 17th century; ships first crossed the Atlantic to Brazil on the Northeasterly Trades, followed the Brazil Current south to pass the Doldrums, and then picked up the Westerlies to cross the Atlantic again, where they could encounter Tristan da Cunha. The Dutch East India Company required their ships to follow this route, and on 17 February 1643 the crew of the Heemstede, captained by Claes Gerritszoon Bierenbroodspot, made the first confirmed landing. The Heemstede replenished their supplies with fresh water, fish, seals and penguins and left a wooden tablet with the inscription "Today, 17 February 1643, from the Dutch fluyt Heemstede, Claes Gerritsz Bierenbroodspot from Hoorn and Jan Coertsen van den Broec landed here.".

Thereafter, the Dutch East India Company returned to the area four more times to explore whether the islands could function as a supply base for their ships. The first stop was on 5 September 1646 on a voyage to Batavia, Dutch East Indies, and the second was an expedition by the galliot Nachtglas (Nightglass), which left from Cape Town on 22 November 1655. The crew of the Nachtglas noticed the tablet left by the Heemstede on 10 January 1656 near a watering place. They left a wooden tablet themselves as well, like they also did on Nachtglas Eijland (now Inaccessible Island). The Nachtglas, commanded by Jan Jacobszoon van Amsterdam, examined Tristan da Cunha and Gough Island and made rough charts for the Dutch East India Company. Dutch sailors also stayed on the island for four weeks in 1658, and made their last stop in April 1669, when their idea of utilizing the islands as a supply base was abandoned, probably due to the absence of a safe harbour.

In the 17th century ships were also sent from Saint Helena by the English East India Company to Tristan to report on a proposed settlement there, but that project also came to nothing.

18th century
The first survey of the archipelago was made by the French corvette Heure du Berger in 1767. Soundings were taken and a rough survey of the coastline was made. The presence of water at the large waterfall of Big Watron and in a lake on the north coast were noted, and the results of the survey were published by a Royal Navy hydrographer in 1781.

A British naval officer who visited the group in 1760 gave his name to Nightingale Island. John Patten, the master of an English merchant ship, and part of his crew lived on Tristan from August 1790 to April 1791, during which time they captured 3600 seals.

The first known attempt to climb Queen Mary's Peak was in 1793 by the French naturalist Louis-Marie Aubert du Petit-Thouars, but this was without success. He did collect and catalogue hundreds of plants from this expedition.

19th century
During this time American whalers frequented the neighboring waters, and in December 1810 an American named Jonathan Lambert "late of Salem, mariner and citizen thereof," along with an Italian named Thomas Currie (anglicized version) and another named Williams, made Tristan their home, establishing the first permanent settlement on the island. Lambert declared himself sovereign and sole possessor of the group (which he renamed Islands of Refreshment) "grounding my right and claim on the rational and sure ground of absolute occupancy". Lambert's sovereignty was short lived, as he and Williams were drowned while out fishing in May 1812. Currie was joined, however, by two other men and they began to cultivate vegetables, wheat and oats, and breed pigs.

War having broken out in 1812 between the United States and the United Kingdom, the islands were largely used as a base by American cruisers sent to prey on British merchant ships. This and other considerations urged by Lord Charles Somerset, then governor of Cape Colony, led the British government to authorize taking "possession" of the islands as dependencies of the Cape. The formal proclamation of annexation was made on 14 August 1816. The British wanted to ensure that the French, their repeated enemies, would not be able to use the islands as a base for a rescue operation to free Napoleon Bonaparte from his prison on Saint Helena. Attempts to colonize Inaccessible Island failed.

The islands were occupied by a garrison of British Marines, and a civilian population was gradually built up. Whalers also set up on the islands as a base for operations in the Southern Atlantic.

In January 1817 the first successful climb was made to the peak of Queen Mary's Peak.

A small garrison was maintained on Tristan until November 1817. At their own request William Glass (d. 1853), a Scottish corporal from Kelso in the Royal Artillery, was left behind with his wife, two children and, two masons. Thus was begun the present settlement. From time to time additional settlers arrived or shipwrecked mariners decided to remain. In 1827 they persuaded five coloured women (these were of mixed race: African, Asian and European) from Saint Helena to migrate to Tristan to become the wives of the five desperate bachelors then on the island. Later, African women from Cape Colony married residents in the island. Other male settlers were of Dutch and Italian origin. As a consequence of this history, the inhabitants are of mixed race. DNA studies have shown that the founding men were primarily of European ancestry.

Glass ruled over the little community from 1817 to 1853 in patriarchal fashion. Besides raising crops, the settlers possessed numbers of cattle, sheep and pigs. Their most lucrative occupation was seal-fishing. The island was still frequented by American whalers. In 1856, 25 people emigrated to the United States, out of a total island population of about 100. The next year 45 of the inhabitants removed to Cape Colony. Since then other younger or more restless members of the community have emigrated there; some took to a seafaring life.

The inhabitants settled on the plain on the north-west of Tristan, as it was the only level land. Here a number of substantial stone cottages and a church were built.

After the death of Glass, the head of the community for some time was a man named Cotton, who had served on a man of war ship, and for three years had been guard over Napoleon at Saint Helena. Cotton was succeeded by Peter William Green (anglicised from Pieter Willemszoon Groen), a native of Katwijk aan Zee, who had settled in the island in 1836. During Green's "reign," the economic condition of Tristan suffered by the loss of ship traffic of the whalers. This was largely due to the outbreak of the American Civil War diverting resources. In addition, the Confederate cruisers CSS Alabama and CSS Shenandoah, captured and burned many Union whaling ships. As a result, the number of ships calling at Tristan considerably diminished and trade languished.

With the opening of the Suez Canal in 1869, together with the gradual transition from sailing ships to coal-fired steam ships, the isolation of the islands increased. They were no longer needed as a stopping port for sailing journeys from Europe to the Far East. Most ships went through the canal for a shorter route.

In 1867, Prince Alfred, Duke of Edinburgh and second son of Queen Victoria, visited the islands. The main settlement, Edinburgh of the Seven Seas, was named in honour of his visit.

In October 1873 the islands were carefully surveyed by the Challenger. Captain George Nares recorded that upon the ship's arrival, the men of Tristan came forward offering potatoes, albatross eggs, and other provisions to his crew. The Captain recorded a total of 15 families and 86 individuals living on the island. This expedition also aided two German brothers named Stoltenhoff, in moving to the mainland at Cape Town. They had been living on Inaccessible Island since November 1871. They were the only ones to have attempted colonization of any island except the main one.

In 1880 the population appears to have attained its maximum. In 1885 the islanders encountered disaster. A poor winter had left them short of food, and a boat sent to barter with a ship offshore was lost with all hands—fifteen men. Only four adult males were left on the island. At the same time a plague of rats—survivors of a shipwrecked vessel—wrought much havoc among the crops. The British government planned to remove all the inhabitants to the Cape, but the majority preferred to remain. Stores and provisions were sent out to them by the British government.

The ravages of the rats rendered the growing of wheat impossible; the wealth of the islanders now consisted of their cattle, sheep, potatoes, and apple and peach trees, and the only form of currency was the potato. The population in 1897 was only 64; in 1901 it was 74, and in 1909, 95.

Tristan da Cunha's residents managed their own affairs without any written laws. The inhabitants have been described as moral, religious, hospitable to strangers, well-mannered and industrious, healthy and long-lived. They lack intoxicating liquors and were said to commit no crimes. , there have been no divorces. They were daring sailors, and in small canvas boats of their own building voyage to Nightingale and Inaccessible islands. They knit garments from the wool of their sheep, are good carpenters, and make serviceable carts.

The Society for the Propagation of the Gospel recruited the first missionary to the island, Rev. William F. Taylor, who served from 1851 to 1856. After his departure, the Bishop of St. Helena attempted to establish an Anglican mission on the island from 1866 onward, and this post was finally filled by Lewis Carroll's youngest brother, the Reverend Edwin Heron Dodgson, who arrived on the island 25 February 1881. Shortly after his arrival he recorded 16 families and 107 individuals living on the island. Reverend Dodgson returned to England in February 1885 and attempted to arrange for the evacuation of the Tristan, meeting with Prime Minister, Lord Salisbury, citing dangerous isolation, but the evacuation was deemed impracticable. Following a disaster at sea that killed fifteen islanders, a large proportion of the working men, Dodgson returned to Tristan in 1886 and remained until December 1889.

20th century
In 1906 the islanders passed through a period of distress owing to great mortality among the cattle and the almost total failure of the potato crop. The majority again refused, however, to desert the island, though offered allotments of land in Cape Colony. Similar proposals were made and declined several times since the question was first mooted in 1886.

A series of Anglican missionaries served the island parish: Rev. J. G. Barrow and his wife Katherine (1906–1909), Rev. H. M. Rogers and his wife Rose Annie (1922–1925), Rev. R. A. C. Pooley (1927–1929), Rev. A. G. Partridge (1929–1932), Rev. Harold Wilde (1934–1940).

On 12 January 1938, by Letters Patent, the islands were declared a dependency of Saint Helena. Prior to this, passing ships stopped irregularly at the island for a period of mere hours.

During World War II, the islands were used as a top secret Royal Navy weather and radio station codenamed HMS Atlantic Isle, to monitor U Boats (which needed to surface to maintain radio contact) and German shipping movements in the South Atlantic Ocean. The only currency in use on the island at this time was the potato, and islanders labouring to construct the station were paid in kind with naval supplies for their own use, such as wood, paint and tea. Money was introduced the following year, as was the island's first newspaper, The Tristan Times. The first Administrator, Surgeon Lieutenant Commander E.J.S. Woolley, was appointed by the British government during this time.

The second Duke of Edinburgh, the husband of Queen Elizabeth II, visited the islands in 1957 as part of a world tour on board the royal yacht Britannia.

In 1958 as part of an experiment, Operation Argus, the United States Navy detonated an atomic bomb 100 mi high in the upper atmosphere about 175 km southeast of the main island.

The 1961 eruption of Queen Mary's Peak forced the evacuation of the entire population via Cape Town to wooden huts in the disused Pendell Army Camp in Merstham, Surrey, England, before moving to a more permanent site at a former Royal Air Force station in Calshot near Southampton, England, living mainly in a road called Tristan Close. In 1962, a Royal Society expedition went to the islands to assess the damage, and reported that the settlement Edinburgh of the Seven Seas had been only marginally affected. Most families returned in 1963 led by Willie Repetto (head of the ten-person island council) and Allan Crawford (the former island welfare officer).

21st century
On 23 May 2001, the islands experienced an extratropical cyclone that generated winds up to 193 kph. A number of structures were severely damaged and a large number of cattle were killed, prompting emergency aid from the British government.

In 2005, the islands were given a United Kingdom post code (TDCU 1ZZ) to make it easier for the residents to order goods online.

The St Helena, Ascension and Tristan da Cunha Constitution Order 2009 was made by Her Majesty the Queen and the Privy Council on 8 July and came into operation on 1 September 2009. The new Constitution replaced the 1988 version and among other changes limited the Governor's powers, included a Bill of Rights, established independence of the judiciary and the public service and formally designated the Governor of St Helena as, concurrently, the Governor for Ascension and Tristan da Cunha. It also ended the "dependency" status of Ascension and Tristan da Cunha on St Helena.

On 4 December 2007 an outbreak of an acute virus-induced flu was reported. This outbreak was compounded by Tristan's lack of suitable and sufficient medical supplies. The British coastguard in Falmouth co-ordinated international efforts to get appropriate medicines to Tristan to treat the virus. Tristan's elderly population and the very young were most at risk; however, only four elderly people were hospitalised. Royal Fleet Auxiliary Vessel RFA Gold Rover upon reaching the island with the required medical supplies found no emergency and the islanders in good general health.

On 13 February 2008, fire destroyed the fishing factory and the four generators that supplied power to the island. Backup generators were used to power the hospital and give power for part of the day to the rest of the island. Power was on during the day and early evening and candlelight was used the rest of the time. On 14 March 2008, new generators were installed and uninterrupted power was restored. This fire was devastating to the island because fishing is a mainstay of the economy. Royal Engineers from the British Army worked on the harbour to help maintain it, as everything comes and goes by sea. This was supported by a LSDA vessel Lyme Bay from the Royal Fleet Auxiliary. The concrete topping put in place has subsequently been badly damaged and on-going repairs will be required to keep the harbour from breaking apart in winter storms.

On 16 March 2011, the Maltese-registered freighter MS Oliva ran aground on Nightingale Island, spilling tons of heavy fuel oil into the ocean. The crew were rescued, but the ship broke up, leaving an oil slick that surrounded the island, threatening its population of rockhopper penguins. Nightingale Island has no fresh water, so the penguins were transported to Tristan da Cunha for cleaning. The Greek captain and his 21 Filipino crew stayed in Edinburgh of the Seven Seas and assisted the islanders in their work.

In November 2011 the Volvo Ocean Race boat Puma's Mar Mostro headed to the island after the mast came down to meet a supporting vessel in the first leg between Alicante (Spain) and Cape Town (South Africa). This event put the archipelago in the world press that were reporting the race, making it known to a larger public.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: History of Tristan da Cunha


text:
Normal matrix

In mathematics, a complex square matrix $A$ is normal if it commutes with its conjugate transpose $A*$:
 * $$A \text{ normal} \iff A^*A = AA^* .$$

The concept of normal matrices can be extended to normal operators on infinite-dimensional normed spaces and to normal elements in C*-algebras. As in the matrix case, normality means commutativity is preserved, to the extent possible, in the noncommutative setting. This makes normal operators, and normal elements of C*-algebras, more amenable to analysis.

The spectral theorem states that a matrix is normal if and only if it is unitarily similar to a diagonal matrix, and therefore any matrix $A$ satisfying the equation $A^{*}A = AA^{*}$ is diagonalizable. (The converse does not hold because diagonalizable matrices may have non-orthogonal eigenspaces.) Thus $$A = U D U^*$$ and $$A^* = U D^* U^*$$where $$D$$ is a diagonal matrix whose diagonal values are in general complex.

The left and right singular vectors in the singular value decomposition of a normal matrix $$A = U D V^*$$ differ only in complex phase from each other and from the corresponding eigenvectors, since the phase must be factored out of the eigenvalues to form singular values.

Special cases
Among complex matrices, all unitary, Hermitian, and skew-Hermitian matrices are normal, with all eigenvalues being unit modulus, real, and imaginary, respectively. Likewise, among real matrices, all orthogonal, symmetric, and skew-symmetric matrices are normal, with all eigenvalues being complex conjugate pairs on the unit circle, real, and imaginary, respectively. However, it is not the case that all normal matrices are either unitary or (skew-)Hermitian, as their eigenvalues can be any complex number, in general. For example, $$A = \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \end{bmatrix}$$ is neither unitary, Hermitian, nor skew-Hermitian, because its eigenvalues are $$2, (1\pm i\sqrt{3})/2$$; yet it is normal because $$AA^* = \begin{bmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{bmatrix} = A^*A.$$

Consequences
$$ $$

The concept of normality is important because normal matrices are precisely those to which the spectral theorem applies:

$$

The diagonal entries of $i = 1$ are the eigenvalues of $A$, and the columns of $U$ are the eigenvectors of $A$. The matching eigenvalues in $Λ$ come in the same order as the eigenvectors are ordered as columns of $U$.

Another way of stating the spectral theorem is to say that normal matrices are precisely those matrices that can be represented by a diagonal matrix with respect to a properly chosen orthonormal basis of $A = UΛU^{*}$. Phrased differently: a matrix is normal if and only if its eigenspaces span $Λ$ and are pairwise orthogonal with respect to the standard inner product of $Λ$.

The spectral theorem for normal matrices is a special case of the more general Schur decomposition which holds for all square matrices. Let $A$ be a square matrix. Then by Schur decomposition it is unitary similar to an upper-triangular matrix, say, $B$. If $A$ is normal, so is $B$. But then $B$ must be diagonal, for, as noted above, a normal upper-triangular matrix is diagonal.

The spectral theorem permits the classification of normal matrices in terms of their spectra, for example:

$$

$$

In general, the sum or product of two normal matrices need not be normal. However, the following holds:

$$

In this special case, the columns of $C^{n}$ are eigenvectors of both $A$ and $B$ and form an orthonormal basis in $C^{n}$. This follows by combining the theorems that, over an algebraically closed field, commuting matrices are simultaneously triangularizable and a normal matrix is diagonalizable – the added result is that these can both be done simultaneously.

Equivalent definitions
It is possible to give a fairly long list of equivalent definitions of a normal matrix. Let $A$ be a $C^{n}$ complex matrix. Then the following are equivalent:
 * 1) $A$ is normal.
 * 2) $A$ is diagonalizable by a unitary matrix.
 * 3) There exists a set of eigenvectors of $A$ which forms an orthonormal basis for $AB = BA$.
 * 4) $$\left\| A \mathbf{x} \right\| = \left\| A^* \mathbf{x} \right\|$$ for every $AB$.
 * 5) The Frobenius norm of $A$ can be computed by the eigenvalues of $A$: $ \operatorname{tr} \left(A^* A\right) = \sum_j \left| \lambda_j \right|^2 $.
 * 6) The Hermitian part $A + B$ and skew-Hermitian part $UAU^{*}$ of $A$ commute.
 * 7) $UBU^{*}$ is a polynomial (of degree $U^{*}$) in $A$.
 * 8) $C^{n}$ for some unitary matrix $U$.
 * 9) $U$ and $P$ commute, where we have the polar decomposition $n × n$ with a unitary matrix $U$ and some positive semidefinite matrix $P$.
 * 10) $A$ commutes with some normal matrix $N$ with distinct eigenvalues.
 * 11) $C^{n}$ for all $x$ where $A$ has singular values $1⁄2(A + A^{*})$ and has eigenvalues that are indexed with ordering $1⁄2(A − A^{*})$.

Some but not all of the above generalize to normal operators on infinite-dimensional Hilbert spaces. For example, a bounded operator satisfying (9) is only quasinormal.

Normal matrix analogy
It is occasionally useful (but sometimes misleading) to think of the relationships of special kinds of normal matrices as analogous to the relationships of the corresponding type of complex numbers of which their eigenvalues are composed. This is because any function of a non-defective matrix acts directly on each of its eigenvalues, and the conjugate transpose of its spectral decomposition $$VD V^*$$ is $$VD^*V^*$$, where $$D$$ is the diagonal matrix of eigenvalues. Likewise, if two normal matrices commute and are therefore simultaneously diagonalizable, any operation between these matrices also acts on each corresponding pair of eigenvalues.
 * The conjugate transpose is analogous to the complex conjugate.
 * Unitary matrices are analogous to complex numbers on the unit circle.
 * Hermitian matrices are analogous to real numbers.
 * Hermitian positive definite matrices are analogous to positive real numbers.
 * Skew Hermitian matrices are analogous to purely imaginary numbers.
 * Invertible matrices are analogous to non-zero complex numbers.
 * The inverse of a matrix has each eigenvalue inverted.
 * A uniform scaling matrix is analogous to a constant number.
 * In particular, the zero is analogous to 0, and
 * the identity matrix is analogous to 1.
 * An idempotent matrix is an orthogonal projection with each eigenvalue either 0 or 1.
 * A normal involution has eigenvalues $$\pm 1$$.

As a special case, the complex numbers may be embedded in the normal 2×2 real matrices by the mapping $$a + bi \mapsto \begin{bmatrix} a & b \\ -b & a \end{bmatrix} = a\, \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} + b\, \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}\,.$$ which preserves addition and multiplication. It is easy to check that this embedding respects all of the above analogies.

title: Normal matrix


text:
Gauss–Markov

The phrase Gauss–Markov is used in two different ways:
 * Gauss–Markov processes in probability theory
 * The Gauss–Markov theorem in mathematical statistics (in this theorem, one does not assume the probability distributions are Gaussian.)

title: Gauss–Markov