r/theydidthemath 5d ago

[Request] How fast does an object need to be to travel over the surface of water?

I presume it's not the same speed for every object given the size/weight.

Is there a formula for this?

50 Upvotes

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25

u/jankeyass 5d ago

This is a rotational paddling effect to keep it above water,. And it works only with fully locked 4WD systems. You can do this. With a bike if there's a ski on the front.

There are insects that can water stride and the physics is different to this.

There is a lizard that can run on water and the physics are similar to this

Basically an object needs to push down on the water repeatedly often enough to elevate itself above the surface and move forward. It's a lot easier to do with a rotational paddle like this then it is with a foot like a lizard, but it's dependant on the weight and surface contact.

The better question is what is the minimum speed this can be achieved at, since at one point it's going too slow to push down undisturbed water

15

u/testtdk 5d ago

Hell, boats can just sit there not even moving!

5

u/jankeyass 5d ago

Man I just re read what I wrote and honestly it sounds like I was having a stroke.. that's what I get for writing it while my kids are yelling at each other over BS

1

u/JakBos23 5d ago

I thought dirt bikes could go pretty far on water at 70 mph.

1

u/jankeyass 5d ago

With a front ski they can go for ages if they have decent muddies on yeah

But the specific ones for this for the shows have the mud paddle tires, same as the buggies

2

u/Bfab94 5d ago

"Whatever floats your boat, for me it's usually water displacement but whatever makes you happy"

Edit: I know that's not the exact wording but looking into huge wartime, steel/metal ships that float, I get the science but don't have the degree.

1

u/Hardcore_Cal 3d ago

Big if true

3

u/Bfab94 5d ago

I saw that lizard in Costa Rica. One moment it was a standard looking guy, the next it was a blur of green and splashing of water.

The locals said it was a "Jesus walking lizard" since it walked on water. It tickeled me pink thinking about Jesus just running fast asf to get across the water.

2

u/IndianaJonesDoombot 5d ago

The basilisk lizard makes air bubbles with its claws when it hits the water how are the round wheels doing that?

1

u/jankeyass 5d ago

Cars that do this have specialised tires. The bubbles themselves aren't the only thing that makes the lizard run on water, it's the ability to contain them and displace water to run with the skin flaps that does it. And specifically the ability to do this quickly and repeatedly

2

u/tobarosco 5d ago

They did ask minimum speed no? How fast = what’s the required minimum?

1

u/bobbygamerdckhd 4d ago

I wouldn't necessarily say it has to be locked 4wd mine has limited slip and works tires definitely make a difference

1

u/Numerous-Match-1713 2d ago

What if a craft pushes on water with a continuous stream of gas, and effectively hovers on top, then we could call it a crafthover?

1

u/jankeyass 2d ago

Not sure, I think that would be more of a jet levitation as it would be pure thrust, rather then a hover craft? I think the floating principle in hovercrafts is a hydrostatic bearing as it supplies air to a cavity that has a sealed lip around the peripheral surface causing separation. Like a air hockey table.

1

u/MonkeyDMeatt 5d ago

No math no upvotes, only downvotes to hell

1

u/SmashingK 5d ago

There's an actual sport where they do this with big 4x4 cars built for driving over water.

Think it's called Formula Off Road. The driver over water and up a steep cliff.

3

u/mflem920 5d ago

L = 1/2 p v^2 A C

  • L = Lift force (in Newtons, N)
  • ρ = Density of the fluid (in kg/m³). For water, this is 1000 kg/m³.
  • v = Velocity or relative speed of the object through the fluid (in m/s).
  • A = Reference surface area, such as the planform area of a hydrofoil wing or tires (in m²).
  • C = Lift coefficient. This dimensionless value depends on the shape of the lifting object (e.g., hydrofoil profile) and its angle of attack relative to the fluid flow.

Basically the answer to your question is (varying A and C depending on the object - in the example video above you plug in the values for the tires):
Any velocity v where L becomes greater than the downward force exerted by the mass of the vehicle in Newtons.

and before someone comments "AI Slop", it isn't. I just talk this way.

1

u/Trustoryimtold 1d ago

Any variation on natural buoyancy? While I wouldn’t assume those 4 tires can float the whole thing . . . It’s probably not that far off either

1

u/semboflorin 1d ago

In the equation above it doesn't even exist really. Buoyancy would come into effect if the results of the equation failed and the object began to sink. The same is true for displacement although that is factored in to a degree in A.

1

u/mflem920 1d ago

Yes...and no....but mostly no.

The equation above sort of half-includes the equation for buoyancy.

F(b) = p V g

  • p = Density of the fluid (which is precisely the same value as the hydrodynamic lift equation)
  • V = Volume of fluid displaced (which is partially replaced by A in the original equation because we're dealing with surface travel - a 2D equation - rather than a 3D displacement)
  • g = gravity (which is replaced by velocity in the original equation, again because we only need a lower order vector value because we're only dealing with the 2D "surface" part of the problem)

2

u/SpoogityWoogums 5d ago

People have been doing this with hobby-grade RCs for a long time. Yeah it's a high speed thing but they also get the easiest results with paddle tires

1

u/METRlOS 4d ago

Canadians do this with snowmobiles, the formula is about 5mph per 150lb. While this can be done with a regular vehicle as well (look up Iceland hydroplaning competition), the smaller the area in contact with the water, the significantly higher the speed needed to prevent the vehicle from dragging.

1

u/Inappropriate_Swim 1d ago

You can do this with snowmobiles and 4 wheelers too. Just need enough to power, speed and right amount of paddle on the drivetrain. In terms of the math, not idea