dave42

Thanks, FB. Now, i'll have to educate myself. That'll take awhile, but you opened a door. I appreciate that.

As to bike handling, I couldn't agree more. I'm pretty good with it, indeed, surprising myself sometimes. Sometimes not. Keeping oneself light in the saddle and on the bars is the key, i think. Body tension is generally not good.

Anyway, time to learn some new math.

FBinNY 

It's easier than it seems at first glance. The downhill force on a bike is equal to the total weight X the sine of the slope angle. Slopes expressed as percentages, which are the tangent of the slope angle, so you need a trig table and can read straight across to convert the %slope to the sine (you don't need the angle itself).

But it's even easier because for the range we're mainly interested in the sine and tangent are pretty close. So it's total weight X % of grade, to get the downhill force to be overcome. Converting that to a torque is equally easy. Consider the non slipping point of contact as the fulcrum, and the forces to be acting on the rear axle and the torque = weight X slope% X wheel radius. (approx). Then it's all about working through the gears if you care about things like chain tension, or pedal pressure.

Note, that these calculations are static, or assume a steady force moving you up the hill. But we're not electric motors with steady torque. Since we apply force only part time, I'll make an assumption that the pedal torque approximates a sine wave peaking when the cranks are horizontal & zero when vertical. Since we need toe average torque to equal the static condition, I'll move the sine wave up accordingly and assume a peak of double the average. (this is easier to visualize if you draw it).

So 200# bike and rider on a 20% grade, needs 40#ft (12" radius for easy math in ones head) average or 80#ft peaks.

This is rough, but I compared results to my own experienced climbing steep hills with a fixed gear and it's pretty close to the "stall point" where it's impossible to turn the pedals by standing on them.

Of course one can do the exact math, but this follows my rule for good answer fast vs. precise answer later.

Note -- this is a quick "napkin" analysis, and I could easily have missed something. So if Prathmann is around, I'd appreciate a quick check.

dwmckee

I use one of these on our tandem to measure grade. A heck of a lot easier:



A plumb bob will give you the vertical. A level will give you the horizontal or the vertical. You would need something else to measure the slope of the road in relation to the horizontal or vertical reference wouldn't you?

FBinNY 

You don't need both a plumb and level, just the level. But you do need a pair of scales at right angles. You can use one of these with a long straight edge of known length. That gives you a fixed horizontal, and a measurement for the vertical. But I agree that a calibrated bubble slope indicator is much easier, and lighter. (except it doesn't go beyond 20%). I guess you could square it up to read -10% when level so you can measure climbs to 30%. (though the relationship isn't linear)

BTW- I just stumbled on this app for smart phones. Stand on the hill, sight along the edge like you would a r-fle to someone upslope and snap --- instant angle. I don't know if it reads in degrees or tangents (percentage) but it's so easy that you can't go wrong.

dwmckee

The bubble thing is just so easy though. I put it on the stoker bar to entertain my son in the absence of an ipad. "Hey Ross, how steep is this?"

"About twelve percent Dad, wait a minute , fourteen, now twelve again."

We can Start a conversation a hundred times a day that way. I don't really care what the grade is anyway but the conversation starter is always good.

FBinNY 

I guess you mised the part where I agreed that the bike mounted slope gauge was easier.....

dwmckee

Didn't miss it. Just agreeing with you and restated it.

dave42

Yep, a steel ruler. Or the ruler on my leatherman. My ruler is the park tool one with the soke guage holes and what all. The ends are rounded, i.e. it's a foot plus some. hence the plumb bob, which is actually a string with a nut tied on the end of it.

I get the string length, then measure the string.

You don't have to measure the slope.

Just rise over run. So, 2 vertical(rise) divided by 12horizontal(run) would be a 16.67% grade.

wphamilton

I am not he, but I'd be more inclined to use the root mean square than half. (Think RMS value of voltage sine wave, about 71%).

It is the peaks that he's concerned about though, as with most of those disagreeing with me. It's pretty obvious that if you took a long enough lever and slammed it down against a bike's momentum you could damage something - peak torque. But consider with a steady power output - the most you can manage for example - against the bike's resistance to motion and disregarding peaks - and simplify that to a steady speed, it seems to me that your force is inversely proportional to cadence which is proportional to the lever arm on the back gears, which means the average torque is unchanging.

wphamilton

You'd really need to integrate the function describing the instantaneous slope and then calculate it for a larger range, although just smoothing out the instant values might be reasonably close. I wanted to DIY one but all I could come up with for digital readings was a bearing in a curved tube with contacts, or several mercury switches. It would be big and look gawd-awful with my fabrication skills, and still approximate, so I've always concluded that what you have is as good, estimating in your head.

Sensitive enough accelerometers would work by measuring changes in slope - it's tempting to investigate phone apps for this. But you've got the calibration problem with inertial measurements (small deviations quickly add up and require re-calibration of the setup), harder than it might appear at first glance.

dwmckee

This little bubble thing actually works fairly well. It varies around as you lean and accelerate but if you watch for a few seconds you can average it out in your head pretty well. We are not using it to conduct scientific experiments or to track gradient over time. Just for occasional something to talk about while riding. $25 bucks and bolt it to the bars and done. Some GPS devices now calculate grade for you but I do not think they are really any more accurate, and who wants to go back and look at old rides and study the archived gradients you are riding anyway? I'd rather just spend my spare time riding instead of doing that...

md11mx

As a suggestion, don't forget that there are 24" wheels also.
Cheers,
David in Alaska