Fly Me to the Moon … With Elephants\!

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Saturn V Thrust

Now, using what we learned, let’s return to the Saturn V. The whole goal of this rocket is to produce enough thrust to lift off the ground and accelerate as it moves up. According to this useful Wikipedia page, the Saturn V produced a thrust of 35.1 million newtons.

That’s HUGE. For comparison, the jet engine on a Boeing 737 has a maximum takeoff thrust of about 120,000 newtons. You’d have to fire nearly 300 of them at once, pedal to the metal, to generate that much force. My little cart would have to shoot more than 800 million balls per second to match up.

Thrust can also be specified in pounds. That 35.1 million newtons would convert to roughly 7.9 million pounds of force. Not by accident, that’s somewhat more than the 6.5 million–pound weight of the fully loaded rocket. The “more” is what allows it to accelerate upward.

Now we can estimate the rate of fuel usage. That page I linked to above lists the total fuel for the first stage at 2.16 million kilograms, with a burn time of 168 seconds. That gives us an average mass rate of 12,900 kilograms per second.

We’re almost done! All that’s left is to convert from kilograms to elephants. There’s a neat trick to do this, which you can use in almost any situation.

In general, to change the units on a number, multiply it by a fraction that is equivalent to 1. So in our case, let’s say a bull elephant has a mass of 6 tons, or 5,000 kg. We can multiply our mass rate of fuel depletion by the fraction (1 elephant)/(5,000 kg), as shown below.

If you look just at the units in the expression below, you’ll see that we can cancel the “kg” on the top and the bottom and we end up with 12,900/5,000 elephants per second, or:

Illustration: Rhett Allain

That’s not all. We can also calculate the speed at which these elephants must be ejected. Using our number for thrust, along with the mass rate (in kg/s), I get an elephant ejection speed of 2,721 meters per second—about 6,000 miles per hour.

Video Analysis

So let’s check the film! I can use my favorite Tracker video analysis software to estimate the mass rate and ejection velocity in the animation. For the mass rate, I count about 6 elephants in 0.3 seconds, or 20 elephants per second. Hmm … that’s a lot higher than my 2.58 per second. The creator of this animation must be using smaller elephants. Either that or I miscounted. (It’s not easy to count ballistic elephants.)

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