# What is the terminal velocity of a sperm whale?

In my understanding, terminal velocity is primarily a function of the mass:cross-section area ratio. So since bigger things generally have a bigger ratio, I imagine that something as massive and aerodynamic as a sperm whale has got to have a pretty high terminal velocity.

Given enough distance to fall, how fast could a sperm whale go? Would it break the sound barrier?

I am not interested in the terminal velocity of a bowl of petunias.

670 m/s

Is this sperm whale skilled in freefall techniques? Will he be falling stably, belly-to-earth? Or will he try for a head-down “max track” position?

Well, a big sperm whale is about 60 feet long, has a head about 8.5 feet in diameter, and weighs 50 ton.
The whale looks a lot like an airfoil, which has a drag coefficient of about 0.045.
It also looks a bit like a prism, with a Cd of 1.14.

According to this Calculation of Terminal Velocity for a skysurfer:
mg = 1/2(Fl)(v)(v)(S)(cd)

m = mass = 100,000 pounds (!!! it’s not me, it’s the calc website)
g = 32 ft/sec^2
Fl = mass density of the atmosphere Mass:0.00236 slugs/(ft3) (standard value)
S = cross sectional area = 56.7 square feet.
cd = drag coefficient = 0.045 or 1.14, depending on shape of whale.
v = terminal velocity.

Plugging in the numbers for a wing shaped whale (cd = 0.045) gives a terminal velocity of** 22,230 mph.**
A prism shaped whale (cd = 1.14) would max out at a mere 4415 mph.

A couple things are made very obvious by these figures.
1: The exact shape matters A LOT.
2: The weight of the whale will cause it to fall at a pretty good clip regardless of the drag coefficient.

If these numbers are even close to right, and there are some very odd units involved in the calculation, your sperm whale would burn up from atmospheric friction long before it reached terminal velocity.

It can be calculated relatively easily.
This site gives the drag coefficient as 0.35. The rest of the problem should be elementary. I’ll run the numbers tomorrow if nobody’s gotten to it by then.

I’m pretty sure it won’t break the sound barrier, since the drag coefficient is a function of Mach, and is maximum at Mach 1.

Mach 30? Something’s funky.

We need to get MythBusters on this!

Seems that way to me too, but 100,000 pounds is a lot of whale.
I didn’t like that mass density unit either. Who calculates in units of slugs per cubic feet?

[quote=“Squink, post:4, topic:462891”]

A couple things are made very obvious by these figures.
1: The exact shape matters A LOT.
2: The weight of the whale will cause it to fall at a pretty good clip regardless of the drag coefficient.

QUOTE]
My whale had a lot bigger head than your whale. Also the Cd is dependent on, among other things, how smooth the outside is. Per Wikipedia sperm whales have a bunch of knobs all over them, so my Cd was bigger.

Couldn’t one use a drag coefficient from a little boy-type bomb? I mean, the evolution of a whale and the design of a bomb are both bent on almost the same purpose: moving easily through a fluid medium with a particular orientation. Does anyone have a good drag coefficient for a bomb or large missile?
(Squink and Santo, its answers like those that make me love the dope!)

So we could orbit a whale but not get them up to escape velocity. Wel that’s a relief. They’d be out in the universe blabbing all our secrets if we let them.

Bunch a blow holes.

Now, what’s the terminal velocity of a bowl of petunias?

Oh No. Not again!

Why, because we’re geeks?
Here’s a pagethat shows drag coefficient versus Mach. I thought it peaked at 1, but it’s actually at about 1.5 or so. I think we could get a pretty reasonable assumption if we used the round nose projectile.

I wrote a bit of code in MatLab several years ago that used an identical graph. We were shooting a 10,000 pound projectile as vertical as possible at about Mach 4. I was supposed to get an estimate of the closest we could expect it to land to the launch site, as well as how high it would go. I created a lookup table in MatLab to be able to vary the drag coefficient as the projectile slowed to a stop, and then tumbled back down to earth. We don’t need a lookup table for this problem, a simple iteration would suffice.

Hancock could tell you something about whale aerodynamics, assuming he even remembers it, which is iffy.

I think the problem is with your slugs, you probably have to divide it by gravity before you put it into your equations. Here’s what I end up with:
%% Terminal Velocity of a Sperm Whale

clear
clc
m = [52 80 130] * 1000; %130 metric tons, kg
g = 9.81; %m/s^2
rho = 1.2; %kg/m^3
d = [2.1 2.5 2.9]; %m
A = pi * d.^2 / 4 %m^2
Cd = .55;

Vt = sqrt(2 * m * g ./ (rho .* A * Cd))
Where 52, 80, and 130 are values for an average sized whale, the largest one around today, and the largest theoretical one before whaling made them endangered, respectively. 2.1 is given as the average diameter, I guestimated 2.5 and 2.9 The answers are:

668, 696, 765
all in meters per second.

.55 is the drag coefficient based on the chart I linked to at Mach 2.

Note the first number is virtually identical to the one SandyHook posted, although I wish they had shared their inputs.

ETA: For those wondering, the ‘%’ sign means that MatLab ignores everything after it, while the ‘.’ means that the matrix is multiplied element wise instead of using rules of linear algebra.

African or European?

Just because we’re talking about sperm doesn’t mean we’re talking about swallows.

Can’t believe no one has brought up the obligatory bowl of petunias to go along with the whale question.

(Psst, check post #11 and the great response in post #12.)

Doh! Missed it. :smack: