# Determining the step size, walking speed, and running speed of a bipedal, digitigrade humanoid species

In determining what units of measurement my fantasy species would have, I've run into the problem of figuring out what length a step would have, how fast their normal gait would be, and how fast they could run. They're around 2,60m tall (8,53 feet) and their limbs are longer than a human's, especially the legs, which are approximately 1,80m (5,9 feet) long. They are digitigrade, with the "bend" at their knees, and have a general foot anatomy somewhere between a human and animals like dogs or cats.

How do I determine the length of a single step? I've tried scaling up my own step but that doesn't look right to me. Walking on my toes, bending my knee, and making my step as large as possible, I reached 84cm, which scaled up by percentage would be 139cm (4.6 feet)for my species, but that's not including the difference of leg length and that number seems too short, anyway. I found different formulas online, one of which would have their footsteps be 44.6cm (17.56in), another 70cm (27.56in), all of which also feel too short when I look at e.g. ostriches with their 3-5m (10-16 feet) per stride -- which I shouldn't, since they have a different limb configuration, but the numbers still make me question my measurements and google.

And from there, how do I determine how fast they could walk and run? Digitigrade legs theoretically mean faster walking and running speed, plus the proportionally longer legs should also affect speed, not to mention the general size difference between a human and one of them.

Very approximate numbers would suffice. Their society is neolithic, so exact numbers for measurements aren't used. The answer is likely "it depends on their muscles" but I'm basically working off the very broad and unscientific idea of "same as human except where it concerns digitigrade walking".

The difference between a plantigrade/digitigrade human and a fully digitigrade creature with longer legs like yours will be greater than just the leg and stride length.

Humans have thick, heavy, muscular legs. This has consequences, in that the legs' lower center of gravity means that the muscular effort required to swing them back and forth in the non-weight-supporting part of the gait cycle is greater than that of animals with thinner legs.

Digitigrade (and unguligrade) creatures concentrate their muscle mass high in the leg, and have relatively slender lower legs and feet, and link muscles to bones by long tendons that run through a series of biological pulleys to the bones upon which they exert their force.

The consequence of this is that with the centre of gravity higher in the limb, the limb can swing more rapidly in the unsupported part of the gait cycle, and therefore the animal may take longer steps.

Why is this? The gait cycle is not only a matter of applying force to the ground in order to propel the creature in the other direction, but also to return the limb to the position for the start of the next step. The more easily the limb swings forward, the longer the stride may be, as it takes less time and effort to return the limb to the beginning of its gait cycle.

So, if the average human leg is around 90cm and has a similar walking stride length (coincidentally an equilateral triangle), this gives a stride angle of around 60°. A digitigrade creature with legs the same length as a human's may be able to have a longer stride because they can have a greater stride angle, perhaps up to 70-90°. However, when running, there are (by definition) also unsupported periods. In other words, the creature effectively jumps from foot to foot as it runs, and the faster the creature travels, the longer these unsupported periods are.

As to how to estimate speed... that's difficult without knowing the exact weight distribution within these creatures' limbs. However, we could expect that with 1.8m long limbs that they might have a walking stride length as long as 2.5m (with a limb angle of 90°, multiply $$\sqrt{2}$$ by 1.8... I'm not going to get into the math here) if they were power-walking, and a running stride length of 3-4m with unsupported periods. As humans have a running stride length of 1.5-2m, this is about twice that of a human. This might give a sprinting speed of roughly twice that of a human (30-44 kph), in the range of 60-88kph.

• Thank you so much for the detailed explanation and the different numbers! That's exactly what I was looking for but I'm neither good at math nor at estimations like that. Your explanation really helped me picture it Dec 14, 2023 at 7:51

It depends on the muscles and mode of locomotion. So really it's up to you.

Kangaroos have digitigrade locomotion for instance and can do 9 metre bounds and travel at 50km/h and they're roughly human size.

Lions can do 70km/h, cheetahs over 100km/h but they're not bipeds.

Walking like we do just doesn't make sense for digitigrade animals, so either locomote on all fours or hop like a kangaroo.

If you must, then you can measure stride length easily by walking a set distance, dividing the number of steps you took by 2 and divide that number into the distance. Half that and you have the step length as well.

• I was thinking upright motion like humans, perhaps leaning forward a lot more for balance, but still on twos. That's mostly an aesthetic choice, however. I tried using different formulas, as I said, but I'm not sure how to change a human's stride to that of one of my species, given the different leg structure and longer limbs. Scaling things updoesn't seem right. Dec 14, 2023 at 7:48