I was out riding and suddenly found the need to measure an area of land. I didn’t have a tape measure with me but as I was riding my fixie I decided to use the number of complete pedal revolutions.

1) The area was 9 complete revolutions by 25 complete revolutions (a bit like north Africa at the moment)

2) The drive train is fixed at 34 teeth front and 18 teeth rear.

3) The rear wheel is a 26″.

4) The tyre is a Trailraker 1.9 if that matters

I am guessing Pi comes into the calculation somewhere but if you think you can work out the maths involved then you probably know what Pi is anyway.

>>>>>>>>>>> 9 by 25 in Pedals = X by Y in metres.

Please provide the correct values for X and Y. You may start now, no conferring.

Bonus point if you can supply me a method for calculating a % slope with no measuring equipment.

1 crank rev. gives you 34/18*pi(3.14)*26 (ish) inches.

% of slope is 4

This is great. Mrs PixelMix is always asking me to come up with questions for her classes (she’s a maths teacher). I’ll get them on this shortly as a “lesson starter”.

I reckon this is fairly easy to work out with 5 minute and a blank bit of paper.

Y = 9*(34/18)*pi*Diameter
X = 25*(34/18)*pi*Diameter

I have no way of knowing what the actual diameter is,as there are too many unknown variables.

26 X 34/18 = 49.1 gear inches. So 1 complete rev=49.1 inch travelled? Doesn’t take into account the tyre though I don’t think?

Is that chicken and ham pi or apple pi?

Taxi………

Other than tyre which is about 5cm from rim to the ground, what other variables are missing?

1 crank rev. gives you 34/18*pi(3.14)*26 (ish) inches.

What is that in Metres?

The percentage of the slope is unknown at the moment because I haven’t a clue how to measure it. The 9×25 is the area I think I have to play with. It is a continuous gentle slope which is about a chestnut tree and a third difference between top and bottom

Precise diameter of wheel after it is built, height of tyre (which is a function of the pressure), then there is the deformation of the tyre because of the riders weight.

The only thing in the formula that has dimensions is the diamter so the output units will be the same as the units you used to input the diameter, so the forumla you quoted would be in inches.

Mmm, Pi….

Only 2 weeks until Pi day.

Bonus point if you can supply me a method for calculating a % slope with no measuring equipment.

Guessing/magic.

Only 2 weeks until Pi day.

Pfft, Americans.

Everyone know that it’s in July, approximately.

Assuming that a 26″ wheel is actually 26″ in diameter, including the tyre, then 9 x 25 cranks = 35.27 m x 97.97 m

As for % gradient, assuming the average horse chestnut tree is between 14-28m in height, and you give a chestnut tree and a half in height gain, lets take a ball park figure of 31.5m height gain.

31.5m height gain over 97.97m is the equivalent of a 32.153% gradient. There is a large margin of error due to the various possible heights of your chestnut tree.

Precise diameter of wheel after it is built, height of tyre (which is a function of the pressure), then there is the deformation of the tyre because of the riders weight.

a) Wheel is about 26″ or at least near enough for these calculations.
b) Height of tyre, including reduction for deformation is about 5cm, again, near enough for these calculations

The only thing in the formula that has dimensions is the diamter so the output units will be the same as the units you used to input the diameter, so the forumla you quoted would be in inches

c) You now have centimetres in answer b so can I have my answer in those please or preferably metres as I asked originally

🙂

Flying Ox gives the answer I needed while I was typing.

For my calculations I will assume 25M x 100m and a 25% gradient*

I know these don’t actually match his answer but are accurate enough and easier for maths going forwards

Cheers

Before: “Please provide the correct values for X and Y.”
After: “Ahhh, sod it. This’ll do.”

😆

Take your bike out to a slabbed pavement. Paving slabs will be 450, 600, or 900mm. I take it your sense of perspective is good enough to decide which. Ride one revolution and you should be able to work it out accurately enough for your requirements.

Hth

I guessed 20m x 80m and about 20% so smudged my numbers with yours and made my maths easy. 😉

Now, what type of track / feature / enjoyment area do I build in such an area?