(Distance measured / height) * 100??? Is this correct?

Question

I have an exercise that tells me to face the wall and bend until my knees touches the wall without lifting my heel, then measure the max distance from my big toe to the wall without my raising my heel. the purpose of this exercise is to determine if there is a problem with my foot.

So if there are three of us who has done the exercise, with different height 5'9 (me), and two other friends who is 5'3 and 6'2. Is it reasonable to that I divide measurement result from the exercise over height * 100 ((exercise result / height) * 100) to get fair value where I can compare result to my friends.

I am not good with english, so forgive me if this looks confusing.

Answer 1

If you want a fair comparaison between you and your friend, you might want to compute the ratio:

$$ r = \frac{\text{Distance from big toe to heel}}{\text{Distance from heel to knee}} $$

This ratio is important if you want to compare your result with your friends. Ideally, you'd want to find a friend with a similar (close) ratio to yours.

Once you do that, measure the shortest (not the longest as mentioned in original post) distance to the wall for both you and your friend. Then you can divide those distances by your respective heights, this will give you two values you can compare.

As a final note, unless this is a purely theoric exercice, I would advise you not to overthink it and just wait to see what your doctor has to say about your results =)

EDIT : In the perspective of coding an app, here might be a good pseudo-code :

# get the user inputs
height = int(input())
feet = int(input())
shin = int(input())
distance_to_wall = int(input())

# Compute the ratio and index
ratio = shin/feet
index = distance_to_wall / height

From there, as you gather data you might want to plot a graph with x=ratio, y=index with mean values, healthy range, and so on. You might also want to think about logging the date of the measurement so a user could see his progress as he's working on his foot condition.

Good luck =)

Answer 2

There are two cases.

If the result of this exercise is somewhat random for each person, then in this case, you would probably want to just take the mean, since you'd need more people to do any reasonable analysis.

If the result of this exercise is somewhat correlated to height, e.g. taller people get a bigger distance between their toe and the wall, then you might want to create a line of best fit $D(x)$ and measure other people against the line.

So in your case, you are assuming that height has nothing to do with the distance measurement, so if that is true, then what you're doing should be fine.