Crank to Wheel Dia. Ratio Calculation

Unicycles and Equipment
1

In my youth, all mathmatical formulas stuck the first time.

Not the case anymore.

Could someone (simply) explain the ratio equation to figure the similar effort required to ride different wheel diameters?

For instance: a 24" with 89mm cranks feels like/rides like a 26" with 150mm cranks. (my intuitive guess only)

A 36" Uni with 150mm cranks = 29" Uni with ?? cranks.

2

Just divide one by the other. That is the ratio.

If you keep your units (wheel dia in inches, crank length in mm) then you’ll have funny numbers but you can compare them to each over

For a true ratio just use inches for the crank length or mm for the wheel and divide the wheel diameter by two.

A 24" with 89mm is like a 26" with… 26 x (89/24) = 96mm.

There are quite to few other factors to how a different wheel or crankset feels but I’m not sure if you could put those factors in an equation

3

Thanks

Therefore, a 29 with 125mm is “like” a Coker with… 36 x (125/29) = 155mm cranks.

Close?

This is good because I’ll be riding along side a Coker with 150s on occasion.

4

Re: Crank to Wheel Dia. Ratio Calculation

Memphis Mud wrote:

> Could someone (simply) explain the ratio equation to figure the similar
> effort required to ride different wheel diameters?

Once again this has been ‘cranked over’ by users on rsu before. Here is
a link to the previous posts. Mikefule “the king of cranks and wheels”
has summed it up nicely here.

Check it out.
http://tinyurl.com/9kul

Cheers,
Jason

5

King of Cranks and Wheels, eh? I try. <humble>

The biggest problem is that we generally speak about wheels in inches, and about cranks in millimetres.

1 inch = 25.4 mm

So to convert a crank length into inches, DIVIDE the length in mm by 25.4

To convert from inches to mm, MULTIPLY by 25.4

For example:
127mm crank divided by 25.4 = exactly 5 inches.
102mm crank divided by 25.4 = 4.01 inches (say 4 inches!)

For future reference:
89 mm = 3.5 inches
102mm = 4 inches
110mm = 4.33 inches (4 and a third)
125mm = 4.92 inches
127mm = 5 inches
140mm = 5.5 inches
150mm = 5.9 inches
170 mm = 6.7 inches
175mm = 6.9 inches

Given all the other variables and approximations, you won’t go too far wrong if you work on 25mm = 1 inch.

Now, which part of the wheel is important? As long as you are measuring a length (as opposed to an area or volume) it actually doesn’t matter, mathematically, as the ratios will remain ‘in proportion’. You could choose to work with the diameter or circumference.

However, I feel it is ‘logical’ to use the wheel RADIUS.

The radius is the distance from the centre of the wheel to the edge. It is half the diameter.

The reasons I say use the radius are:

  1. If you think of the hub as the fulcrum (which is not quite accurate when the uni is being ridden) then one arm of the lever is the crank, and the other arm of the lever is the distance from the fulcrum to the ground: the wheel radius.
  2. Of the three options (radius, diameter, circumference) the radius is smallest. This makes small differences in ratio more obvious at first glance. (If this isn’t clear, just trust me.)

So, there are two ways to work out the ratio.

Assume a 20 inch wheel and a 5 inch crank.
The wheel radius is therefore 10 inches.

So the crank:wheel ratio is 5:10
The wheel:crank ratio is 10:5
(Worry about percentages later.)

It actually doesn’t matter which method you use as long as you are consistent. One way, you’re saying the crank is half as long as the wheel radius; the other way, you’re saying the wheel radius is twice the length of the crank.

I prefer to work with crank:wheel. This is because when I started to think about these things, I was concerned by how easy the unicycle would be to mount, idle and stop. Thinking this way, then a BIGGER number = MORE LEVERAGE = GOOD.

Thinking the other way (wheel:crank) the ratio shows how much FURTHER the tyre goes than the pedal. That means a BIGGER number = MORE INCREASE = FASTER (but less control).

It really doesn’t matter, so unless you have a reason to change, stick with my approach.

So far, we’ve:

  1. Established the crank length in inches. (mm divided by 25.4)
  2. Established the wheel radius (Diameter divided by 2)

Now all we do is:
Crank divided by radius.

e.g. 5 inch cranks, 20 inch wheel (10 inch radius)
5 divided by 10 = 0.5

I prefer to think in percentages, so I multiply the answer by 100.

Thus:
5 divided by 10 = 0.5
0.5 x 100 = 50
I say 50% (which we all know is a half)

Go back a bit and we started with 5:10
5:10 is the same as 1:2 (we’ve simply divided each side by 5)
1:2 is ‘the same’ as 1/2
1/2 is the same as 50%

So I’ll run through that with a different uni:
127 mm cranks. 24 inch wheel.

127 / 25.4 = 5 inch cranks
24 /2 = 12 inch radius.

5/12 = 0.417
0.417 x 100 = 41.7
So we have a ratio of 41.7%

So we know this uni will be harder to idle than the first example (5 inch cranks, 20 inch wheel = 50%, remember?) but it will be faster than the first example.

So, how do we set out to match the ratio on a different uni? How do we make a 28 ‘just like a Coker’?

Coker = 150mm cranks, 36 inch wheel.
That’s 6 inch cranks (near enough) and 18 inch radius.
6/18 = 0.333 (a third!) and times 100 = 33.3%

So a Coker has a ratio of 33.3%

And we want a 28 with a ratio of 33%
The radius is 28 / 2 = 14 inches.
We want 33% of that.
33% is 33/100

So, 14 x 33 / 100 = 4.62

So we need 4.62 inch cranks.

4.62 TIMES 25.4 = 117mm

So our mini Coker needs cranks around 110 to 125 mm.

Does any of that help?

6

Re: Crank to Wheel Dia. Ratio Calculation

Mikefule,

Let me just say I appreciate the time you took for another
comprehensive writeup to make this absolutely clear.

Klaas Bil - Newsgroup Addict

“When someone asks you, ““A penny for your thoughts”” and you put your two cents in . . . what happens to the other penny? - George Carlin”

7

Re: Re: Crank to Wheel Dia. Ratio Calculation

Me too.:smiley: