themidge wrote: ↑
Tue Apr 24, 2018 8:59 pm
Yeah, I should have been more clear about 'need', 'helpful' is better. My question still stands though, some people seem to put such low gears on their bikes I struggle to see how they could ever need/prefer them, regardless of fitness.
It's really simple:
10% grade or more
70 rpm or more
FT or less
3w/kg or less
If a cyclist has half the w/kg as a pro, then they would probably find the same gear useful on slopes half the grade. These people are also relatively less adapted to make anaerobic efforts, mash through things, and not skin and bones which hurts their w/kg, I know lots of people here are very strong capable riders who dedicate their life to cycling, especially since dropping $10k+ on a bike is not unusual here. I don't mean to offend but it is a little mind boggling how much people can be unaware that there are many, indeed most cyclists, are considerably weaker than them and also do not make their life revolve around bicycles or training, even certain kinds of people that buy super record (because they can).
I also personally have great difficulty turning 39x25 on 20% without momentum carrying me through. I beleive is not just an issue of fitness, but also has to do with the way steep grades interact with pedaling using gravity, in other words, climbing by standing on pedals, not climbing by pulling on the bars.
If you plot out:
sin(2pix/d+pi)*c+gx (for the other side of the crank)
d = meters of development
c = crank length in meters(165mm: c=0.165)
g = grade (20%: g=0.20)
Let us do some common sense checks to make sure the plot is accurate. d=5, c=0.170, g=0.00. It takes 5 units of x for one complete cycle, y tops out at 0.170, and -0.170, so far so good. d=5, c=0.000(tracking bb axle), g=0.20. When x=5, y=1. That seems reasonable, 1m rise over 5m run is 20%. Any engineers are free to correct me if I made a mistake.
Let us qualify dead zone where the slope for both plots is 0 or positive. At 0%, the only dead zones are TDC.
For me on 39x25 on 25mm on 20% is:
1 full sin cycle is 3.29m. Between x=0 and x=3.29, slope is equal to 0 at (1.183, 0.364) and (2.107, 0.294). Note that there is a negative slope between these two points, meaning the pedal is traveling downwards.
The difference between y values, the distance the pedal moves downwards in one sin cycle, 0.364-0.294=0.070. Only 70mm, compare this to 0% grade where the pedal would be moving downwards 330mm. That is quite a large difference. Remember that work = force (gravity in this case) * distance.
Let us also consider the parts where both plots have positive slope, in other words, both pedals are moving upwards. I'm just going to cheat here and double the value I get from my previous 2 points 2(2.107-1.183)=1.848. This is the x range that one of the pedals is moving down. 1.848/3.29 = 0.5617. Only 56.2% of crank rotation has a pedal moving down. 43.8% of crank rotation or forward movement, both pedals are moving up. 43.8% of standing on the pedals dead zone.
Doing the same analysis with 34x32:
Gives us the points (0.719, 0.293) and (1.521, 0.155). The pedal moves down 138mm, nearly twice as much as 39x25. 71.6% of crank rotation or forward movement has one of the pedals moving down. Only 23.4% is standing on the pedals dead zone.
This second component has absolutely nothing to do with fitness, except that you can compensate for it by pulling on the bars. I am curious what effect an oval chainring might have on these figures, but I am in no mood at the moment to attempt calculation, or create a spreadsheet for every gear combination until I have some time to check my math again. I may have fudged the numbers somewhere, but I beleive this is correct in principle. Note that longer cranks would help, indeed because of more leverage as people have said in the past. I remember one time trying different gears on the same short climb from a stop at the bottom, and there was a point where it seemed like the pedal was actually pushing me back when I tried to stand on the pedal.