# Finding phase velocity for froude number scaling

So I am calculating phase velocity of a wave for Froude number scaling for model testing of a boat. I got data from Lloyd's Rules saying for the specific sea area I did $$H_s=3.6\text{ m}$$ and $$T_z=6.8\text{ s}$$.

Assuming a regular, progressive wave (this is where I might be wrong) and using the deep water relationship of $$\lambda = \dfrac{gT^3}{2\pi}=712.5\text{ m}$$.

Wave celerity $$v=\dfrac{\lambda}{T}=\dfrac{712.5}{6.8}=104.7\text{ m/s} = 377\text{ km/s}$$? Am I doing this right? Are ocean waves supposed to be that fast?

• I assume that's meant to be 377 km/h, not km/s, right? If so, please edit your question to correct that typo.
– Wasabi
Nov 30 '18 at 20:14

I'm not sure where did you brought the 'deep water relationship' in here. If you're dealing with usual water wave (gravity, surface, linear, and close to sinusoidal wave form), then the relationship you'd need to use will be dispersion relationship.

$$\omega^2 = gk\tanh(kh)$$

As you're assuming deep water, it becomes: $$\omega^2 = gk$$

Which leads to almost exactly same equation you came up with, but one less power of T:

$$\lambda = \dfrac{gT^2}{2\pi} = 72m$$

and phase velocity of 10.61 meter/second.

(Actually, your original calculation, with $$T^3$$ was incorrect. That should have give you wave length of 491 meter, instead of 712 meter)