Standing start torque profiles

I have found an interesting article with some torque profiles of a track cyclist during a standing start measured at 200Hz using a SRM Torque Box. I have found this very interesting because nearly all of the studies about pedaling in cycling are conducted at constant cadence and power outpout because they want to study stationary state efficiency but this one shows how the torque is affected by a variable cadence and power. As you can see the shape of the torque profiles are pretty much the same independently of the cadence so the steady state pedaling model is a good aproximation for acceleration, even though, a cadence-torque plot could be useful to obtain an even better approximation. I will consider these torque profiles for a standing start load case, the severer that a bicycle frame should withstand but first I need to develop a model to calculate total pedaling forces from propulsive forces. Here you can see the article:

I don't know who is the rider that generated those torque profiles but his peak torque is about 450Nm. It's a really high value so I will scale later those plots depending on the load case. I have read that Sir Chris Hoy can generate up to 600Nm of peak torque during an standing start, something really impresive. You can see him making his chain suffer here:

That's all for today. Greetings

Forces at pedals. Fatigue. Summary

In this post, I want to take a critical approach to the method that I have utilized to obtain the force plots that I have shown in the previous posts. To do this,  I will list the process that I have followed and the assumptions that I've done to obtain these plots:

• First, I obtained a mathematical relation between the foot angle and the crank arm angle based on a 60fps video of a random cyclist pedaling round at an aproximated cadence of 60rpm. Both the method used to calculate the angles and the fitting routine induced errors.
• Next, I used previously published data of tangential and normal forces at pedals of a cyclist pedaling at 84rpm in order to obtain a mathematical expression of these two components of the force.
• Following, I calculated the x and y components of the force at pedals using the mathematical expression obtained previously and the relation between the foot angle and the crank arm angle. Doing this, I assumed that: 1) the pedaling style of both cyclists is the same and that 2) in the 60-84rpm range, the relation between angles is constant. This two considerations are questionable and they will modify to some extent the final result.
• Finally, I used vectorial decomposition to obtain all the other plots.

In the two following plots you can see some small errors induced by this method:

The correlation between the plots that I have posted and previously published data of pedaling forces at lower wattages is good so I will consider my results as valid. If I don't found pedal force profiles for higher wattages I will scale these ones to replicate higher load cases. Considering the variety of different pedaling styles and some of the testing methods utilized in the industry, I think that this approach is solid. Obviously, putting a professional sprinter in a ergometer pedaling at different power oupouts and positions will be a better way to obtain these forces profiles but that isn't an option for me. Finally, a last graphic of the pedal force components that a crank arm must resist for the indicated power outpout (radial force sign defined by the theory of elasticity):

That's all for today. Greetings