Ideologue

I read that the maximum amount of torque momentarily produced by a professional (racing) cyclist is in the region of 1,000 Inch Pounds. That is 83.3r Foot Pounds, or 112.984 829 333 Newton Meters.

A 250cc motorcycle I used to ride only produced around 20 Newton Meters, so is the 112+Nm figure really an accurate one for the maximum torque a human can produce on a bicycle? It seems rather high to me. But then considering a rider with a mass of around 100kg standing up on the pedals and allowing his entire weight to push down on 175mm cranks (with a turning circle of 1099.6mm). This rider without even trying, and merely allowing gravity to pull his mass down and turning the cranks in the process, will exert approximately 539.35Nm of force through the bottom bracket spindle.

Rider’s weight: 981 Newtons
Distance cranks turned (at pedal): 0.54978 Meters

Riders weight divided by distance crank turned?

Now 500Nm of force sounds like a huge amount to me for a rider to exert, even for just a few seconds. That is a similar amount an average juggernaut produces. I think I have my sums wrong.

What do you make of this?

CTAC

Torque is force times radius. Assuming crank length 175mm and rider's weight of 140 pounds, that gives us 80ft.lb or 109 NM torque when rider is standing and crank is *parallel to the ground*. The average torque will be much lower, something about 50NM.

Ideologue

Thank you for clearing that up for me! It is surprising to learn that a rider is capable of producing 5 times the torque of my old motorcycle.

chrisvu05

except that you are only factoring in the rider's weight and not the actual sum of forces being applied to the the crank. If you do a free body diagram of the system, you have the weight of the rider, the force applied by the rider pushing the down stroke, and gravity for simplicity all summed at one point on the pedal down stroke. So assuming your 140 pound rider is a pro cyclist who can most like single leg press over 400 pounds on each down stroke (probably a modest number) You get the sum of the forces in Nm as 109 + 311.5 (probably modest) + gravity (negligible) so you are looking at roughly 420 Nm of torque

chrisvu05

wow i did all that work and then i realized that you only asked for just the rider's weight to be included but just so you know that isn't the maximum torque that can be applied to the crank as it is just one of the torques/moments applied to the crank. The definition of Torque is the sum of the torques/moments which are found by Force x radius of each of the forces (rider weight, pedalling force, and gravity) acting on the crank

CTAC

But... How?!

chrisvu05

when you stand on your pedals are you just letting your body weight do the work? or are you using your body weight as well as leg extension (ie muscle force) to do the work. How do you think Robbie McEwen can out sprint me when he is 150 lbs and I"m 250lbs. If it was just body weight on the down force I would kick his a$$...you have to factor in the force of the downstroke (which is much larger than the force of the weight) as well as the weight.

CTAC

Muscle works like a spring. It pushes pedal down and pushes body up. Have you heard about Newton laws? If force is greater than the body weight you are just bouncing up. Yes, you can compensate for that with your arm holding handlebars tight, but not by much.

As for the Robbie, he is faster *average* moment is greater then yours, not maximum.

chrisvu05

So tell me, why is his moment greater then mine if all that is involved is the weight of the cyclist. It is faster because he is applying a greater down force on the pedal because of his superior leg strength. The down force ( hamstrings/quads/glutes/calves) as well as the weight contribute to an accelleration of the crank arm which in turn transfer this acceleration the rear wheel. When you push down on the pedal, your body only travels up before you break the force needed to overcome the force that the pedal is applying back to the leg. Here is a quick experiment....hop on your bike and go for a quick interval standing sprint....don't do an all out 100% sprint maybe just an 80% sprint then do it again but all out 100% standing sprint....wow, you miraculously go faster....why? because you applied more force to the downstroke of the pedal. Your weight didn't change did it? What changed? The force of the downstroke which led to an increase of the force on the crank which all acted at a point (the pedal for simplicity) which is a give radius from this center of rotation which when you apply a greater force at a given distance.....you have by definition (Force x radius) a Greater Torque!!!

chrisvu05

I guess what I'm trying to get at here is how is his "average" moment greater if weight is the only differing factor? That would mean his average moment for all time assuming constant weight would be 140lbs x the Crank length...so my average moment would be 250 lbs x the Crank Length.....once again I"m producing more of a moment....so how is his average moment going to be greater than mine without applying enough down force to overcome the force that I'm putting on the cranks?

chrisvu05

one more scenario that might help....Say I maintain my current leg strength but I weigh 140 lbs....I go up against McEwen who we've been saying is 140 lbs.....why is he still faster then me? Because his leg strength (down force) is greater than mine...which contributes to a larger moment at the pedal leading to an increased angular acelleration of the crank arm which causes a faster spinning of the chain and thus a faster rear wheel which leads to a great speed.

Ideologue

Thanks for your reply. That's a lot of torque those little 2mm wide sprockets have to deal with!

chrisvu05

no problem...it's funny cause I just spent so much time trying to defend my answer I had to reread what I originally said. I hope i got it right cause this stuff was part of my undergrad (Biomedical Engineering) so either I nailed it...or it has been 5 years since I took the related class freshmen year (2001) and I need a refresher...lol

I<3Mountain Dew

Not to mention....motorcycles (mostly sport bikes) aren't made to be torquey at all, they rely on horsepower and high rpm.

Plus such a small bike (250cc) is also probably a 2 stroke, which creates even less torque.(compared to a 4 stroke.)

chrisvu05

Mountain Dew...you just made my night...me and the other guy just spent a good part of our evening arguing backe and forth and you come in make a simple to the point statement that could've probably stopped the discussion before it started....thanks for the laugh...it got me out of my "brain-on" mood so I can finally go to bed.

Ideologue

Well I am interested in this topic mainly due to two reasons: I am designing a bike (and wish to do a good job of it) and I am going to study mechanical engineering next academic year. I suck at the moment, but a few months intensive learning should supply me a firm hold on the basics!

Ideologue

Mine was a 4-stroke (KLR 250), and it certainly did like to rev a lot (4,000 RPM = 40mph). Its maximum power output was around 21 - 27hp.

Mothra

One of the reasons you can exert more force than your body-weight is that you'll pulling up on one side while pushing down on the other. The back-muscles is also used when pulling up on the bars to counteract the upward movement of the body. So you won't automaticaly launch yourself off the bike if you apply more than your body-weight. Of course, it takes years, decades of training in order to get the brain/muscle-coordination to spin smoothly while sprinting.

The other thing you have to consider is the gearing. It's really torque at the rear wheels that makes the bike move. Actually thrust at the contact patch is what counts. So take torque at the crank, run it through the gear-ratios, divide out radius of rear-wheel and you get linear thrust at the contact patch. You'll notice that the bike's gearing divides (reduces) the torque, while a motorcycle's gearbox multiplies (increases) the torque from the crank.

Finally, it's power that's the real determination of speed. Which is torque X RPM, so the faster you spin, the more power you make. A motorcycle's torque multiplied by 9000rpms is gonna generate a heck of a lot more power than a human at 90rpms. You can take McEwen's 1700-watt output and work backwards through the gearing & RPMs to arrive at his torque@crank and realise the guy's a monster!

operator

Sprinters are putting out what.. 2000w in the TDF sprints? Something around that neighbourhood?

CdCf

Because it takes POWER to go fast, and power is force multiplied by speed, or in this case pedal torque multiplied by rotational rate (cadence). If your torque is indeed higher throughout (which I doubt), his cadence at the lower torque level he is at, is sufficiently greater than your speed.

Let's say a sprint finish for Robbie McEwen requires him to put out 500 W. His gear is 53/11 and he's riding on 20 mm tyres. Let's also assume that the sprint is at 60 km/h. 60 km/h is 16.7 m/s, and the circumference of a wheel is 2.074 m. That means ~8 wheel revolutions per second, and the 4.82 pedal-to-wheel ratio gives us a cadence of ~100, or 1.7 revs/sec. Dividing power by "second-cadence" gives torque, and 500 W / 1.7 r/s = 294 Nm. That's his average torque. Peak torque per half pedal cycle will be higher. How much higher is hard to say.

This was just an example. His actual speed and power during a sprint may well be higher. But you still calculate it the same way.

Albany-12303

One would think that a body-builder with massive thighs could put out more torque than a professional racer (even if it is more a second or two). Much more high twitch muscle.

CTAC

According with this: https://www.mayq.com/Best_european_tr...speed_math.htm
Robbie McEwen will only spend ~240W at 60kmH, assuming no further acceleration, flat ground and 140lb weight.
That gives us about 140Nm average torque. Yeah, he is not just standing on pedals letting gravity do the job

CdCf

According to my own calculations, he'd be in the 600-650 W range to get up to 60 km/h.
240 W would mean 38 km/h by the same math.

The linked page has some major errors in it.

This site, on the other hand, seems to overestimate power a good deal (giving almost 1400 W for the same situation as above). But I suspect the numbers are skewed intentionally too show recumbents in a better light as the site appears to be a recumbent propaganda tool...

CTAC

His *total* power output could be 650W, but only 240W are used for *wheels motion*. He's not 100% efficient. Do you agree?

CdCf

No, I don't agree. I'm only talking about the actual useful power. The power required of an engine were it to replace Robbie...

If we go into total power for the body, we have to multiply the power figures by five, as the cycling efficiency for the body is about 20-21%. However, that only scales the numbers up, but the ratio doesn't change.

About 300 W is the endurance power level for pros at his level, and they're not riding solo for hours at 65 km/h, which would surely be the case if 240 W was sufficient to go 60 km/h...