Here's why pedal-steer is smaller than you think

[billyk]

We've been having a long discussion in the thread "Are you a pusher or a puller?". A whole lotta words got slung around (including mine), without seeming to shed much light.

The thread filled up with chatter about various ways the alternating pedal pushes get balanced. It didn't ring true to me, but I realized I couldn't quite explain it.

Yesterday afternoon it finally stopped raining here in atmospheric-river land and I got a chance to do some riding tests. I wanted to see how much force it takes to counteract pedal steer, and figure out why my experience says "very little".

I first did a bunch of trials that weren't useful because I often ride no-hands and couldn't suppress the muscle-memory of that enough to do realistic push-pull tests.

Then I picked a hill (much) too steep for me to ride no-hands. I rode up it holding the bars with just one hand. There definitely was a push-pull going on, but it didn't seem to need much force compared to how hard I was pushing on the pedals (very hard). How can that be?

There are two pieces to the answer:

1) The handgrips are much further offset from the steering column than the pedals are (ignoring the length of the boom for the moment). On my Q the distance from steering column to the center of the hand-grips is 11.5 inches, and the center of the pedals are about 5.5 inches from the center of the BB. That gives your hands a larger lever arm by a factor of about 2.

That extra leverage means one could balance the torque of pedal-steer with _half_ the force being put into the pedals.

But considering how hard I was pushing to go uphill, what I was doing with my one hand didn't feel like half that.

2) The pedals are far out in front of the bars, on my Q about 28 inches. This turns out to be the main story (see attached diagram; you can read the fine print but it should be comprehensible just looking at the diagram):

The forward-directed off-center pedal push (vector c) can be decomposed into the two perpendicular vectors a and b, which combined give an equivalent force. Vector b is along the line from the steering axis to the pedal center; any force along this line points directly away from the axis and therefore has zero component around the steering axis: it does not contribute any rotation to it (no pedal steer from this).

(This is how you ride no-hands: push slightly outward along vector b.)

The much smaller vector a is the only thing giving pedal steer: its action is to rotate the BB around the steering axis.

Using numbers taken from my Q:
Boom length = 28 inches
Distance from the center of the pedals to the center of the BB = 5.5 inches

A bit of trigonometry (details on request) leads to angle Phi=11.1 degrees, with sin(Phi)=0.193.
That is the ratio a/c, namely the fraction of pedal force (c) that goes into pedal steer (a).

=> Pedal steer is about 19% as large as the pedal forward push due to this aspect of the geometry.

=> When you also include the handgrip distance factor of one-half as in (1) above, the pedal steer that needs to be counteracted by the arms is about 10% as large as the forward pedal force.

It's not nothing, but it is small. It's hardly noticeable in the both-hands pulling that gives more power when sprinting or climbing.

And regarding the push-pull debate in the earlier thread: Yes, you can balance pedal steer either by arm-pulling on the side that your foot is pushing, or arm-pushing on the opposite side. But this only works if you are not overall pulling to strengthen the force you are able to direct to the pedals, that is, if the only use of your arms is to counteract pedal steer. In that case you get no extra upper-body power.

If you ARE trying to use your upper body to gain power, then you need to pull with both hands, slightly alternating the pull from each arm: by about 10%. Like I said, in my experience it is hardly noticeable.

 

[ak-tux]

Excellent explanation.

In addition , when riding hands free, I think, the opposite leg also helps to counter that "a" component of the pedal force to cancel the steering effect.

As you apply more force to climb or accellerate the value of the "a" component also also proportionately increases hence it gets harder(not impossible) to ride hands free.

 

[Henri]

Thank you, I wanted to post something like that there and it was too much work. XD

On your Q is the handle right at the steering axis? On the V20 and S30 (and I think on the current Q45 it depends on your sizing) the bars are way behind the steering axis, so the lever gets worse, whan you want to push/pull, but adds the possibility to shift sideways.

And yes, the more you counter the pedaling force by pulling on the handle bars, the less pedal steer becomes a topic, because there is less relation between bthe front triangle (with the pedals) and the rear frame (with the seat, that you would use for countering otherwise). If you were only able to counter pedaling force with the handle bar, you would automatically distributie the forces through your body accordingly. But I think for that you would then position your body in a way to produce most force / most efficiently and that position might be shifted and you would need to "take the seat with you", so there would be some steering happen after all. Basically it's just another way of looking at the system with another point of reference, but the same thing still happens. So when you say "slightly alternating the pull from each arm". The same stabilizing pulling happens, it just gets drowned out by the pulling to counter the pedaling force.
In the same way when we stard pulling the opposite pedal, we are doing part of the countering there, but this introduces even more steering, so we need more stabilizing - wich we can generate by shifting the handlebar sideways.
I am really getting needlessly lost in complexities of the whole picture now, I guess. Your diagram is good and simple. My mind is just going and going, understanding and simulating the system. There won't be much learning left, when I can finally start riding my future V20-2022. XD

 

[benphyr]

If I am understanding correctly I think the general leg force vector may be directed relatively parallel to the direction of travel (from hip to pedal centreline) making the pedal steer portion even smaller.

 

[billyk]

If I am understanding correctly I think the general leg force vector may be directed relatively parallel to the direction of travel (from hip to pedal centreline) making the pedal steer portion even smaller.

Hmmm. The leg force vector is c: exactly forward. Are you saying that needs modification?
Perhaps it does, but I am simplifying things to make this fit in a 2-d diagram (and 2-d-thinking brain).
Other complications are whether the steering axis is exactly at the handlebars (as @Henri mentions above). In the case of my Q they are, but on some the bars would be further back. Too much for this simple analysis. Mostly, I needed to convince myself that my experience of the alternating pulling being minor was reality-based.

 

[benphyr]

I was right: I was reading the chart wrong.

 

[Doug Burton]

I love to see a force/vector diagram when someone's doing an analysis like this.

My faith in engineering science (as opposed to "SCIENCE") is preserved.

Well done, BillyK.

 

[chicorider]

And as an English major, I tend to take the as-long-as-it-works-and-you-don't-ask-me-to-explain-how-it-works-I'm-good approach. I mean, I know a little bit about physics, such as Alfred E. Newton invented gravity, and that before he did that, apples just kind of floated around in the air, and stuff. It was cool of him to take care of that for us.

 

[JerseyJim]

If you ARE trying to use your upper body to gain power, then you need to pull with both hands, slightly alternating the pull from each arm: by about 10%. Like I said, in my experience it is hardly noticeable.View attachment 12452

I appreciate and accept the vector analysis regarding balancing pedal steer. That's clear and well done.

I still don't understand how only pulling can add additional pedaling force and pushing does not. My experience does not square with this.

 

[xtalbike]

I've also found that pushing on the bars feels like it gives you some extra power in the pedals. A couple of speculations about why: 1) Your back and the seat cushion aren't rigid. Every forward push on the pedals has to compress anything that you're braced against. By pushing on the handlebars you preload this compression so more of the pedal push goes toward propulsion. 2) It's not realistic to ignore the rest of the pedal stroke that's not directed straight forward. Pushing your back down into the seat also helps to preload the weaker push across the dead spot. That preloading is probably a larger percentage of the overall energy going into that weak part of the stroke so it might make a bigger difference. Riding up steep New England hills where I get front wheel slip if I mash there's no question that pushing my back down into the seat helps me get through a climb. Of course sitting up and pulling helps too but is less sustainable on a long climb. Last point: I think pushing on the bars activates your core and engaging your core gives your gluts something to push against so you might get some benefit from more involvement of some big muscles.

 

[Henri]

Pushing the handle bars might also just plant you into the seat more firmly. This might really benefit the stability, for example against rolling off, when sliding the pedals through the dead spot with force.