Z and I carried Fitbit pedometers as we walked so that we could keep track of how many steps we took.

In addition to being really useful for estimating distances, we figured it would be fun to know just how many steps there are in a thru hike between Cape Reinga and Bluff.

Ok, so if you want to cross New Zealand, we can definitively tell you this:

- Z took 4.7 million steps.
- I took 4 million steps.

The difference between us is height. I’m several inches taller than her and have a much longer stride.

The other fun fact this tells you is that since we each destroyed 4 pairs of shoes, you can consider one million steps to be the limit per pair.

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SCIENCE TIME OUT

Assumption: knees do not exist

A person’s stride length is determined by

(1)

`D = 2`

Lsin(theta/2)where

D is stride length

L is leg length

theta is “stride angle,” the angle formed between the person’s legs at full stride

Total distance covered (X) is your stride length (D) multiplied by total number of steps (N). We also know you covered the same distance.

(2)

`X = D * N`

(3)

`X_m = X_z`

(3.1)

`D_m * N_m = D_z * N_z`

(4)

`2 * L_m * sin(theta_m/2) * 4,000,000 = 2 * L_z*sin(theta_z/2) * 4,700,000`

Assumption: Your stride angles were negligibly close during the trip. I happen to know Mike takes big old strides on purpose, but still: assumption.

(5) theta_m = theta_z

So we can simplify (4) to

(6)

`L_m * 4,000,000 = L_z * 4,700,000`

(6.1)

`L_m/L_z = 4,700,000/4,000,000`

(6.2)

`L_m/L_z = 1.175`

So Mike’s leg’s oughta be 17.5% longer than Z’s legs. If we assume you’re equally proportioned, and Mike is 6’6″, that means that Z is 5’6.4″ tall.

Your comment formatter made hamburger of my equations, interpreting text between two * as italics.

Better?

much better

But you forget one thing…I have long legs even for a man of my height.

I hedged on that when I said “if we assume you’re equally proportioned”. As Mike’s leg/height ratio increases relative to Z’s leg/height ratio, Zeina gets taller.

So if we define K=L/H, where L is leg length and H is total height, Zeina’s height is given by

H_z = H_m * (K_m/K_z)/1.175

Zeina says that she’s 5′ 9″. Best if z & m can measure their in-seams.

I’m not gonna measure my legs for your entertainment, Biz.

I dunno, Biz, the numbers say 5’6″. But let’s say for the sake of argument that Z is right and she’s 5’9″. That means the K_m/K_z ratio must be 1.0394, so M’s inseam (measured to the ground, not to the ankle) relative to his height should be about 4% higher than Z’s.

According to the Human Factors Design Handbook, average height-to-inseam ratio is 45% and 50% is considered long-legged. We know M is freakishly long-legged, so let’s assume M has the 50% ratio, and Z’s 4% lower at 48%, which is still above average. That makes Z’s inseam (measured to the floor) 33.1″, and M’s 39″.