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# How Fast Do They Go?

You don't know how many times I'm asked this question, and it's one of the questions in my online FAQ. My quick and dirty answer is a quick walking pace, and that's enough for most people. But it's also a question that can stand additional effort to understand more fully. We all know how fast our subs end up going as a result of motor, battery and propeller combinations, but how fast SHOULD they be going? If we wanted to make a completely scale boat that performs in a scale manner, how fast should we set it up to mimic it's full-scale brethren?

To answer this, we can look to math.

People much smarter than I have created a formula that calculates what scale speed is based on actual speed and a model's scale. This formula looks like this:

Scale Speed = Real Speed / (square root of the scale)

There is an excellent webpage that has not only this information, but also has a calculator that you can use to get your proper scale speed based on the full sized counterpart actual speed and your model's scale, just in case you don't want to do the math yourself.

So, let's look at an example. Let's say you're modeling a 1/72 Guppy II RC submarine. According to many sources, the Guppy was capable of 16 knots submerged speed. If we use the above equation, we get:

Scale Speed = 16 / (square root of 72, or 8.49)

This winds up at 1.89 knots, or 2.2 mph. So.. if you want a perfectly scale boat, operating at perfectly scale speed, your model should do 2.2mph in submerged trim at flank speed.

Since we're talking about speed, we can also take a minute to talk about efficiency. Some submarines are more efficient at cutting through the water than others, and mathematicians have actually created a formula for determining and comparing this. This value is called the Admiralty Coefficient, and here is the low-down:

Admiralty constant – A coefficient used in the preliminary estimations of the power required in a new design to attain the desired speed. It is presented by the formula: where: D = displacement in tons, V = speed in knots, P = shaft power in kW. Values range from 400 to 600, the higher the value the more economic the vessel.

#### C = D2/3 · V3 / P

Again, I found an excellent online resource that has alternate versions of this formula for determining displacement, speed and horsepower, and also has an online calculator you can simply plug your numbers into in order to get the desired value.

What I find most interesting is the relative efficiency of each submarine design. The website actually has a chart of common submarine platforms, and even has a coefficient for torpedoes. Let's take a look!: As you can see, of these designs, the USS Albacore is the most efficient design, almost TEN TIMES more efficient at cutting through water than early WWII fleet boats were and TWICE as efficient as a more contemporary design such as the Sturgeon.

Of course, if you know the actual displacement of your model, the horsepower of your drivetrain, and the the speed you can achieve, you can determine your own model Admiralty Coefficient for your boat. I hope you found this insightful! Bob Martin

the RCSubGuy

bob@nautilusdrydocks.com