Experiment for choosing a bike gear for uphill

[boysathome]

My homeschooled 7th-grade son is doing a science fair project on choosing the best gear to go uphill. After our research, he understands how gear ratio works, how to determine gear ratio, why we need a low gear ratio for uphill and how more force/torque is created on the gear/wheel; thus he is able to make a very good educated hypothesis. However, we are having a hard time determining a way to use an experiment to prove/un-prove his hypothesis.

Originally our research question was: How does changing gears affect distance? But we realized that going uphill was more of his "problem" (if that makes sense). our experiment needs to have only one independent variable (changing the gear). With our dependent variable being distance, we will be measuring tire rotation of back wheel/distance of ONE pedal rotation. Controlled variables: friction, tire pressure, bike weight, pedaling force, incline (none).

I'm unsure if this experiment will clearly illustrate which gear should be used to go uphill. We can change our "research problem" but that is not as appealing to my son.

Would it make sense to use the explanation of an inclined plane to illustrate why we need less back wheel rotation to go uphill? Like an inclined plane, it takes less force pushing something uphill (easier to pedal) but takes more time (more pedaling). I'm not sure if I have this right. Will this experiment work as an answer to our question? if not, could someone recommend a different experiment that would show more clearly why a lower gear is better for uphill? We understand the "whys" mathematically and physically but we need to be able to show it.

[audreyln]

Hello,

This sounds like a fun project and you are well on your way already!

Since the question you are trying to answer is which gear is best for going up hill this is really related to how much force it takes to rotate the pedal rather than the distance the bicycle travels. One avenue you might think about taking is measuring the force to turn the pedal (dependent variable) at different gears (independent variable).

Not sure if there are affordable/easy to use devices out there to measure the force but my initial thought is a something like a hanging scale (luggage scale?) that you could hook onto the pedal and then pull the scale and measure how high the weight (force) gets before the pedal starts to turn or the average weight (force) needed to turn the pedal one rotation.

Hope this is helpful,

Audrey

[boysathome]

that's interesting. i was trying to think of a way to measure force given that a consistent force of power (leg strength) is unreliable.

so are you saying ideally: have the bike on the floor, upright, with pedal at lowest position, attach a scale, pull (by hand) the scale as the pedal rotates and record the "weight" as an "output force needed." and push down (repeat measuring weight or "output force needed"). Each gear would have two reportings (push and pull)? and the one with more force needed would be the most weight registered?

This makes sense since we are looking for the most force.

[bfinio]

Hi,

Jumping in here with another suggestion - rather than trying to set up an experiment where you are putting the bike upside down and measuring force on pedals etc, you can do human trials to measure the amount of time it takes to go a fixed distance uphill with different gears. You could say that whichever gear helps you get up the hill the fastest on average is the "best."

The caveat here is that you will need to figure out how to do the human trials to keep things as controlled as possible. Humans aren't machines - we get tired and we can't control the exact force exerted or RPM of our legs. So you shouldn't, for example, just have one person do back-to-back trials in different gears, because they will get tired and that will affect the results, and since everyone's size/speed/strength is different, some people may get the best results with different gears. But you could have multiple volunteers do the test with breaks in between trials, and encourage them to keep their effort level as constant as possible (since deciding to sprint up the hill as hard as possible for one trial would mess up the results). If you do enough trials and collect enough data, then you should be able to identify an overall trend/average for which gear is "best."

Hope that helps!

[boysathome]

We can only have one independent variable. If he had multiple ppl, it would be more than one variable.

I’m rethinking the uphill part of our question. I’d like to do something with gear inches. That seems simpler.

I’m feeling discouraged about an experiment that answers a question (using the scientific method) using a bike. Is the bike rider considered a control? A argument could be made for yes and no.

For this reason, we were hoping to do something by hand pedal rotation. So that rules out speed and force, right?

[bfinio]

So, backing up a bit, there are a few things to consider here. First, you will need to be careful about any question which asks which gear is "best" or "easiest" because those are subjective terms depending on the rider. Some people might say "best" is the gear that gets you to the top of the hill the fastest. Others might say it's the gear that makes your muscles the least tired when you get to the top, even if it took longer. So if you go that route, you need to carefully define what you mean by "best." If you want to keep it to a single human rider, you would probably just need to keep it to a short hill and give them plenty of rest between trials, so getting tired between tests did not affect the results. You could also control for this by repeating the tests on different days and having them test the gears in different orders (even with rest, they may get progressively more tired, so you would not want to always test the gears in the same order).

The next thing to consider is that you need to be careful extrapolating results from turning the pedal by hand when the bike is upsidedown to actually riding the bike. When you are turning the pedals by hand and the bike is upside down, the only force resisting motion is internal friction in the bike's chain/gears etc. When you are actually riding the bike, the required force on the pedals depends on the weight of the rider, their speed, friction between the tires and the road, and the incline of the hill. So you could, in theory, do an experiment to determine "how much force on the pedal is required to make the wheel rotate at a certain speed?" when turning the pedal by hand with the bike upside down. But you cannot correlate that directly with speed going up a hill.

As for "ruling out speed and force" when doing hand pedal rotation - you can measure the speed of either the pedals or the wheel by counting how many revolutions they make in one minute, which will give you a measure of RPM. Measuring force exerted on the pedal will be more difficult but might be doable. As audreylyn suggested, you might be able to use a spring scale (they should be available online, they are commonly used in physics classrooms), hook it onto the pedal, and use it to pull the pedal by hand. You would need to keep the spring scale perpendicular to the pedal's crank arm when doing this, so the direction of the force you measure is constant.

Either way, I think you should be able to do an experiment with one independent and one dependent variable. Let us know if you have more questions.

[boysathome]

These are all super helpful. We have thought through all those forces (weight, friction, strength etc) and have never wanted to turn our bike upside down to do the experiment. There are many variables contributing to all “forces” on a bike! Whew.

We have decided to change our question to how do gears affect speed. Our research is still applicable and he still understands what *should* happen to speed in diff gears. (Theoretically, if gear ratio decreases, speed should decrease on a flat surface.)

We are planning on using a speedometer over the same distance (or pedal revolutions?) to see which gear he can go get the most speed. I like the idea of repeating the experiment on diff days with the same rider and compiling the results and looking for congruency. Thank you for warning us about “best.” We have considered that but it had not transferred over to the language we were using. So thanks for insight.

Any other thoughts?

[bfinio]

A couple thoughts:

- Even if you aren't going up a hill, the same thoughts about difficulty/force/effort etc for a human rider all still apply. He will have to figure out how he is going to try to control the experiment and ride with the same amount of "effort" for each trial, since we can't mathematically control the exact amount of force exerted by our legs. If you pedal crazy hard in a low gear, you can still go faster than you would with less effort in a high gear.
- One thing we haven't talked about yet is acceleration. It takes some time and distance to get the bike going from a start up to a steady speed. Gear ratio will also affect how easy it is to accelerate (e.g. in a lower gear, it can be easier to accelerate, but your top speed will be lower). So for example, if you only measured the time required to cover a very short distance, the lower gears will seem "faster." You can account for this in two ways: 1) Measure speed over a long enough distance that the effects of the initial acceleration time are minimized, or 2) always give the bike enough time/distance to accelerate to full speed before you start your measurement. (this, of course, provides an interesting alternative experiment - e.g. measuring how quickly you can get to top speed in different gears - but maybe save that one for next year!).