How to Calculate Weight on Pedals from Watts?

[BFC]

Summary: How to calculate weight on pedals?

For example, a bicycle pedal manufacturer might say that their pedals have a max rider weight of 120kg (264lbs). First off, since the rider is sitting on the saddle, I'm not sure how this would really impact max pedal weight? Going forward, these are power meter pedals so they can withstand and report up to 2000w. Maybe I'm over thinking this but the 264 lb rider would only impact the pedals when standing on the pedal, but exceeding the max weight once they start pedaling while standing. So, the question is how to calculate weight from watts? I read this post https://www.physicsforums.com/threads/pedal-force-for-bicycle-43-2mph.444916/ but I think there is a BIG error in the formula. This is because they calculated 1500w (per pedal), but, the way power meters work is that they report both leg totals, so, at 1500w, each leg is only contributing 750w. So their calculated force in that post would be 1/2 of their result. This is better evidenced by single-sided power meters which take left leg power and multiply by 2 before transmitting to the cycle computer.
So, let's say a 164lb cyclist is putting out 2,000 w. Max pedal weight limit is 264 lb so I'm trying to figure out max pedal weight by 164lb + 1000w
How many pounds is 1000w?
Thank in advance

 

[anorlunda]

Summary: How to calculate

How many pounds is 1000w?

Apples and oranges. You can't convert.

When I mount my bike I often start by standing on one pedal. So worst case for the pedal is not when the rider is sitting on the seat.

 

[BFC]

Wouldn't it be something like Ft-LB Force per sec?

 

[anorlunda]

Wouldn't it be something like Ft-LB Force per sec?

Almost, that is power. But ft-LB per sec is not LB. I can see what you're trying to do. Force on the pedal (if constant) times PI times the diameter of the pedal circle has units of work times revolutions per second has units of power. So you want to work back from power to the force.

But the force on the pedal while sitting and pedaling can't be more than the force needed to lift the rider off the seat. Therefore, the biggest force on the pedals comes when the rider's whole weight is standing on one pedal. Perhaps double the rider's weight if he jumps on the pedal.

 

[phyzguy]

Let's try to work it out. Work is force times distance. So if you push down on the pedals with a force equal to a weight of 100 kg, this is 100kg * 9.8 nt/kg is about 1000 nt. The typical pedal stroke is about 25 cm, so each stroke does 1000nt * 0.25m = 250 J of work. If I'm going at a cadence of 100 rpm, this means 200 strokes/minute, so the power is 250J/stroke * 200 strokes/minute / (60 seconds/minute) = 833 Watts. You can ratio up or down from there by changing the force or the cadence. So at a cadence of 100 rpm, 1000W would mean you're pushing on the pedals with about 120 kg of weight. It might be more or less depending on the cadence and how much force you are applying on the upstroke.

 

[anorlunda]

So at a cadence of 100 rpm, 1000W would mean you're pushing on the pedals with about 120 kg of weight.

Now do a free body diagram on a 70 kg rider. What prevents him from being lifted off the seat?

If the analysis was more detailed where both the magnitude and direction of the pedal force was a function of phase, it might reveal more. At some point in the circle, the foot pushes the forward, pushes the rider aft, and the seat of his pants pushes forward. Those opposing forces could exceed rider weight. But at another point in the circle the foot must push straight down and the max force must be approximately rider weight.

Also at some phases in the circle, the pedal force must be zero, making the assumption of uniform pedal force versus time invalid. Note that I am thinking of each pedal separately, not the sum of two pedals.

I suppose hands on the handlebar could oppose the body being lifted in the air.

 

[jbriggs444]

Also at some phases in the circle, the pedal force must be zero, making the assumption of uniform pedal force versus time invalid.

Between toe clips and cleats, you can power through a complete cycle. But yes, uniform pedal force is invalid. Hence elliptical chain rings.

I suppose hands on the handlebar could oppose the body being lifted in the air.

Indeed so.

 

[phyzguy]

I suppose hands on the handlebar could oppose the body being lifted in the air.

Absolutely. A racing cyclist pulls up on the handlebars so that they can push down harder on the pedals. My brother-in-law broke his carbon fiber handlebars during a sprint at the end of a race.

Anyway, I was just trying to make an estimate. Feel free to do a more detailed analysis.

 

[berkeman]

When I mount my bike I often start by standing on one pedal. So worst case for the pedal is not when the rider is sitting on the seat.

A racing cyclist pulls up on the handlebars so that they can push down harder on the pedals.

And when I land jumps on my MTB, pretty much all of my body weight is on both pedals. Flat landers (say "ooof") probably put the most weight on the pedals of all biking situations.

(that's not me in this picture...)

https://betterride.net/blog/2014/hit-big-drops-and-jumps-on-your-mountain-bike/

 

[phyzguy]

One other point on this. Non-cyclists may not realize how hard you have to cycle to generate 1000 Watts. When I'm riding hard, I'm putting out perhaps 200-300 Watts. Tour de France class cyclists can put out an average power of perhaps 400 Watts, and world class sprinters can go over 1000 Watts for brief periods during a sprint.

 

[anorlunda]

Summary: How to calculate

And when I land jumps on my MTB, pretty much all of my body weight is on both pedals.

Wouldn't worst case for pedal max design weight be if you land using one foot, even if accidental? Weight * number of Gs deceleration.

 

[berkeman]

Wouldn't worst case for pedal max design weight be if you land using one foot, even if accidental? Weight * number of Gs deceleration.

I don't think so, only because that would be an instant crash. Ouch!

 

[anorlunda]

I don't think so, only because that would be an instant crash. Ouch!

I don't understand that comment. The OP question related to the required design strength of the pedals. How much force until the pedal breaks off? Crashes are irrelevant unless a broken pedal contributes to the crash.

 

[sophiecentaur]

world class sprinters can go over 1000 Watts for brief periods during a sprint.

I'm not sure how relevant this is. As a secondary Science school teacher, I used to get kids to run upstairs ant to estimate their power output. It was quite common to find that a fit young teenage boy could generate 1kW by running up a flight of stairs between floors (standing start). Admittedly this was for a few seconds of activity but these were not super athletes - just fit boys. I'd expect athletes to exceed this figure significantly.

 

[cjl]

Usually, that kind of data is looked at as power output vs duration it could be sustained for, and apparently, for a reasonably fit, athletic person, 1kW is pretty typical for durations of a few seconds. This of course falls rapidly as duration increases though. Here's a chart with some percentile measurements on it (power output on the vertical axis, duration of sustain on the horizontal)

https://s3.amazonaws.com/cyclinganalytics/static/power-curve-statistics-7.png

 

[berkeman]

I don't understand that comment.

By "instant crash" I mean that the bicycle will fold immediately to the side of the weighted pedal, and the bike and rider will go down pretty much immediately to that side. There will be a little force from the landing on that pedal, but not as much as when the weight is on both pedals for a balanced landing. Gives me the willies just thinking about it...