What is the Top Speed of the Megaladon?

[dean barry]

The megaladon being the extinct super fish, the 100 ft long "shark".
I started with the orca which has a top speed of 30 mph ( 13.411 m/s ) and gave it the same Cd ( drag coefficient ) as a family car, the power then working out at approx 788 kW / 1,056 hp.
The length of an orca is 30 feet, so i figured the Cd for the megaladon at 10.9 times that of the orca, but i need to guess the power of the megaladon, i have used the cube of the length ratio of the two for the calculation and have rated the megaladon at 29.172 MW / 39,120 hp
This led to a top speed of 19.4 m/s ( 43.4 mph )
Comments please.

 

[zoki85]

The length of an orca is 30 feet, so i figured the Cd for the megaladon at 10.9 times that of the orca, but i need to guess the power of the megaladon, i have used the cube of the length ratio of the two for the calculation and have rated the megaladon at 29.172 MW / 39,120 hp
This led to a top speed of 19.4 m/s ( 43.4 mph )
Comments please.

Why didn't you use top speed and hp of great white shark instead?

 

[boneh3ad]

I hope you are fact checking and not just going off of that fake Discovery Channel documentary. 100 feet is essentially twice the maximum length of a megalodon according to actual science.

 

[A.T.]

The length of an orca is 30 feet, so i figured the Cd for the megaladon at 10.9 times that of the orca,

The drag coefficient mainly depends on the shape, not the size:
http://en.wikipedia.org/wiki/Drag_coefficient

How did you arrive at that 10.9 factor?

 

[dean barry]

Youre right, a less sensational length turns out to be 60 feet, so i will base it on that.
The drag co-efficient is fairly straightforward, i based it on two identical shapes but of different size, starting with the forces calculated by the empirical equation for drag force ( f = ½ * d * A * Cd * v ² )
I ended up with :
New Cd value = ( ( new length / old length ) ² ) * old Cd value

 

[dean barry]

Can i point out that the Cd in the empirical equation is fixed and represents the shape only, what i use in mine represents the shape and the size bundled together.

 

[A.T.]

Can i point out that the Cd in the empirical equation is fixed and represents the shape only, what i use in mine represents the shape and the size bundled together.

Okay, that clears it up, but it's not the standard definition of Cd and a bit confusing.

the 100 ft long "shark"...length of an orca is 30 feet, so i figured the Cd for the megaladon at 10.9 times that of the orca,..

New Cd value = ( ( new length / old length ) ² ) * old Cd value

(100 / 30)² = 11.11 not 10.9

Not that it really matters in such a crude approximation, but it made it even more confusing.

 

[dean barry]

Sorry about that, having reduced the estimated megalodon length to 60 feet, the Cd factor is now (2²) 4.0

 

[boneh3ad]

How are you coming up with this scaling? The drag coefficient should be (largely) independent of size. Or rather what is your justification for why you are using that method?

 

[dean barry]

I based the orca Cd on a small car, in the car industry the Cd figure factors in the size as well as the shape.
Back tommorow same time (ish)

 

[cjl]

In the car industry (and many others), they often use the CdA, not just the Cd, which factors in the size and the shape. The Cd alone does not factor in the size in any industry. Also, I would expect the drag coefficient of a fish or whale to be substantially lower than that of a car, due to the much better streamlining. Finally, why do you assume that a shark and a whale have similar power output per unit volume?

 

[A.T.]

i need to guess the power of the megaladon, i have used the cube of the length ratio...

This led to a top speed...

If you scale the power with the cube of length, then you kind of assume that the speeds scale linearly with length (muscle forces scale with the square of length). So you assume what you are trying to find. Can the speed you obtain via quadratic drag be consistent with that assumption?

 

[dean barry]

So its the CdA of a supercar that = 0.40
I assume sea level air density is assumed
So the air drag force (N) of the supercar at 30 mph = CdA * v ² = 0.40 * 13.411 ² = 71.942 N
(thats in air, so * 800 for water = 57,554 N)
Power of the orca then = 57,554 * 13.411 = 771 kW / 1,035 hp

I have no idea about power to size, so i assumed that its proportional to volume, so if you double the length of the orca (which the megalodon is) you get (2 ³) 8 times the power = 6.168 MW / 8,271.4 hp

I think the equation for the megalodon CdA holds good, so :
megalodon CdA (in air, at sea level) = ( ( 60 / 30 ) ² ) * 0.4 = 1.6

By trial and error using what I've got then, i get top speed @ 16.8 m/s ( 37.5 mph )

 

[A.T.]

I have no idea about power to size, so i assumed that its proportional to volume,

But this already assumes that speed is proportional to size, doesn't it? So you are assuming your result. At best you will get out, what you have put in, which is useless. At worst you will get a contradiction with your other assumptions.

 

[Danger]

...the orca (which the megalodon is)...

No, no, a thousand times no.
The megalodon was a shark, as you even pointed out in your initial post; orca's are unpleasant dolphins. They swim (swam?) in completely different ways and their motions are probably as important to speed as any sort of drag coefficient or muscle strength. Fish get their initial blinding burst of speed and a lot of their top speed from the lateral sinusoidal flexion of the body including a large vertical tail, which causes something akin to a cavitation effect along the sides and cuts down on drag significantly. Cetaceans use a slower vertical oscillation with a broad flat tail, hence the term "porpoising" in reference to aeroplanes and such-like. It's like comparing a dragster to a semi.

 

[cjl]

So its the CdA of a supercar that = 0.40
I assume sea level air density is assumed
So the air drag force (N) of the supercar at 30 mph = CdA * v ² = 0.40 * 13.411 ² = 71.942 N
(thats in air, so * 800 for water = 57,554 N)
Power of the orca then = 57,554 * 13.411 = 771 kW / 1,035 hp

Why are you assuming that two wildly different shapes (namely, a large dolphin and a car that isn't even designed to minimize drag) have similar drag? There's really no basis at all for this assumption.
(In fact, after about 30 seconds of googling, I found http://jeb.biologists.org/content/201/20/2867.full.pdf, which is far more relevant to your inquiry than any comparison to supercars)

 

[Danger]

Why are you assuming that two wildly different shapes (namely, a large dolphin and a car that isn't even designed to minimize drag) have similar drag? There's really no basis at all for this assumption.
(In fact, after about 30 seconds of googling, I found http://jeb.biologists.org/content/201/20/2867.full.pdf, which is far more relevant to your inquiry than any comparison to supercars)

Excellent link, Cjl. That's far more than I ever wanted to know about it, actually, but great for the OP. I do, however, find the name of the author somewhat ironic.
I simply don't have the patience to read the whole article, but I suspect that one thing probably isn't mentioned in a comparison among different cetaceans because they all share it while fish generally don't. I might be misremembering, since it's been over 35 years, but think that I read somewhere about cetacean skin being a "laminar flow" material which has a far lower drag effect than a smooth surface.

 

[DaveC426913]

Here is a cool site that shows top speeds of several sharks and dolphins/whales:

http://www.speedofanimals.com/

It would be interesting to plot them all, and see if
a] there is a trend relating length, weight and top speed
b] the trends for sharks and whales are similar

 

[zoki85]

Here is a cool site that shows top speeds of several sharks and dolphins/whales:

http://www.speedofanimals.com/

Sailfish...top speed 110 km/h oo)

 

[DaveC426913]

If one were going to plot this on a 2D graph, one would have to combine length and weight into a single value to put on an axis.

How might one combine these two properties into one to yield a meaningful X or Y axis?
l*w? l/w? Is there a proportion? squaring? cubing? root?

 

[Danger]

That's an excellent link, Dave. I've bookmarked it in my "Technical Research" folder.
The low relative speed of the Mongolian wild ass took me by surprise. I was once acquainted with a Hungarian wild ass, whose speed was about 450 rpm.
I have no idea how the scaling factors would work. My only somewhat similar experience was in trying to explain to people why "The Attack of the 50 Foot Woman" couldn't ever really happen because of the square-cube rule.

 

[dean barry]

Wealth of stuff to chew on, thanks all.
Dean