# Speed of vehicles built by humanoid giants

Let's imagine a race of Giants, with an average height three times that of a normal human being. Let's also imagine that these Giants are completely identical to humans, proportionately speaking... that is, they haven't disproportionately larger or shorter legs, hands, or any other bodypart. Every single segment of their body is three times larger that of an average human.

Let's also imagine these Giants create vehicles, namely chariots and triremes. Those vehicles will be three times larger than the average "human" chariot or trireme. Everything abides by this proportion, be it wheels, horses, sails, ores, etc...

Now, I would like to ask... what would be the speed of said giant chariots and triremes? Would they be three times faster, or would the function of the speed vary in another way with the augmenting size?

• Bet the square cube law messes everything up. Nov 23, 2016 at 21:32
• @Bellerophon about to answer the Q with that Nov 23, 2016 at 21:33
• Also, I doubt that they would be three times faster. A cruise liner isn't three times faster than a yacht but it is hundreds of times bigger. Nov 23, 2016 at 21:34
• @JDługosz: "What is the walking speed of an elephant, horse, mouse?"; This question is irrelevant. It should be: what's the walking speed of a horse, of a mouse-sized horse and an elephant-sized horse? Nov 23, 2016 at 22:52
• Elephants are not scaled-up mice. The legs are different to accomodate the weight. Your people will have legs and arms thicker than the overall scaling factor. Nov 23, 2016 at 22:52

I have to disagree with the others here, yes it is right that the mass would be cubed while the power would be squared, however, strength isn't usually the reason for the speed limit of animals (humans included), instead it is the inefficiency of our limbs at these speeds. For example if you run 20 km/h your foot is pulled forward 40 km/h slowed down set on the ground while propelled backwards until it is 20 km/h slower than you and 0 km/h to ground, than again accelerated forward to 40 km/h.

If you size everything up three times, you would be acceleration a 27 times bigger mass with 9 times the power, BUT you would have to do it only once per 3 times a normal creature has to do, making it actually pretty even. Even better, you have 3 times as much time and space to accelerate your feet.

In the end the heart and bones would be a much bigger factor in the top speed than the up sized mass, because the biggest problem for such kind of creatures would be to keep their bones intact and circulations running. (The heart would have a hard time to keep the blood flowing).

So if you just say the bones are much more durable than ours, the top speed would come down to their hearts abilities to provide oxygen for the muscles, and you would end up with something like elephants. relative fast (about three times as fast as we) walking speeds but lack of the ability to run. In that scenario every creature would be about three times faster while trotting and walking, but just barely, if even, faster than we are when at max speed.

If you also presume the heart can provide the oxygen and the muscles can catch the impact when landing, the limit would be a good amount higher, not three times because wind resistance would become a problem at speeds over 60 km/h but they would be about two times faster.

• The humans that don't stop growing are pretty similarly portioned to the rest of us, and their hearts give out standing well before 20 feet. So some handwaving seems to be required, and you handwave the bones why can't you handwave the arteries further?
– user25818
Nov 24, 2016 at 15:15
• You are correct, there are many more parts in our anatomy that would fail under these conditions, however I think the heart and our bones are a very good example to show problems with bigger sized humans, without going to far off topic. The topic itself was about the speed such sized creatures could archive, not if they are possible. Nov 24, 2016 at 15:21
• Ismalith is correct... the topic was solely about speed, not the feasibility of such humanoid Giants. Nov 24, 2016 at 20:22

Edited based on comments

## The Square Cube Law Has Arrived

Notorious for shutting down numerous ideas on this site, the SCL saw this post and just couldn't resist.

As the dimensions of objects triple, their "muscle power" which correlates with surface area, is multiplied by 9 ($3^2$), but their volumes (spaces taken up) are multiplied by 27 ($3^3$).

Therefore, all people and machines will have 9 times the power pulling 27 times the weight - $9/27$ , or $1/3$ the efficiency! This is bad news.

The horses pulling in this setting require 3x as much energy, but they are scaled up Earth horses with no changes (ex. bigger muscles) to accomodate for these requirements, so they will run $1/3$ as fast.

Yet these horses have 3x the gait, as @mg30rg pointed out.

If normal chariots can reach ~20 mph, these ones will be one third of three times that.

## $20$ mph chariots (that get tired 3 times faster)

The triremes' speeds are harder to calcuate, but it has been estimated that they went about 8.5 mph. The same problem applies here - oarsmen who require 3x the effort are moving a ship 27x as large (volume).

Correct me if I'm wrong, but
$3$ times the initial difficulty to move themselves * $27$ times the size of the ship = $81$ times slower

$8.5$ mph / $81 =$

## ~$0.104938272$ mph trirremes (See below)

Although depending on the exact specifications (is this a larger boat scaled? Smaller? etc) as @jpa pointed out, you may be able to pull off speeds much faster with larger boats. This is because they will meet less resistance in the water.

• Square cube law, ruining stories every day. Nov 23, 2016 at 21:40
• Actually I think the triremes wouldn't be that slow. Accelerating the boat does scale by the cube, but most of the resistance forces scale by the surface area. For example friction with the water and air resistance both depend on surface area, not volume. And wave-making resistance actually gets smaller when the boat gets longer.
– jpa
Nov 24, 2016 at 6:21
• Why muscle power is dependent on surface area? IMHO muscle power is dependent on mass, which is volume, so the power scales with same factor as volume. Now, the cooling area available, that I agree, but it only means that giant horses would be 27-9=16 times as sweaty (gross oversimplification) as ours at same speed. Conversely, the air resistance would be only 9 times higher compared to 27 larger muscle mass, so giant horses would be actually more efficient than regular ones at high speed. Nov 24, 2016 at 9:10
• @Bellerophon Square cube law, ruining stories every day. ...stories? What about ruining reality in the first place? Nov 24, 2016 at 12:46
• @coredump I tried but it didn't scale up well. Nov 24, 2016 at 16:23

They would not be as fast as the "normal-sized" versions. Long story short, they get hit with the downsides of the Square Cube Law.

Let's talk chariots first. You're tripling the size of the riders, the chariot itself, and the wheels, which means you're effectively tripling the weight of the whole system. However, you aren't doing anything about the horses pulling the chariot. In order to apply the same amount of relative power, you'd need to triple the number of horses, at least - once you start adding in multiple horses you start losing efficiency. In addition, the wheels themselves would be at more risk of breaking due to their increased size - the stress on the wheels increases a lot with the increased weight. In order to deal with the increased stress, you'd need to make the wheels wider in addition to taller, but that means adding more weight in general. Net result: slower.

Moving on to the boats.

Honestly, I don't think that a classic Greek trireme would work at all in this universe. The triple-decked oar arrangement doesn't really work so well with the increased size requirements. If people get up to twenty feet tall, the ships would have to be massively bigger than they were in our history.

And that's where the Square Cube Law really bites you. The ship is getting bigger in volume, and the sails/oars are getting bigger by area.

As I'm writing this, @Zxyrra just posted their answer with some of the math behind the Square Cube Law, so I won't repeat the numbers. The end result is that you aren't able to get as much propulsion relative to the weight, leading to lower net speeds.

It's kinda like how you can flick a pebble and it will fly through the air, but kicking a boulder doesn't move it at all.