As a rule of thumb, the power P (in horsepower)
that a ship needs can be modeled by P = d^2/3 • s^3 / c where d is the ship’s
displacement (in tons), s is the normal speed (in knots), and c is the Admiralty
coefficient. If a ship displaces 30,090 tons, has a normal speed of 22.5 knots,
and has an Admiralty coefficient of 370, how much power does it need?
P = d^(2/3) + S^(3/c).
d = 30.090 tons.
s = 22.5 knots.
c = 370.
P = (30,090)^(2/3) + (22.5)^(3/370),
P = 967.42 + 1.0256 = 968.45 hp.
To find how much power a ship needs, we can substitute the given values into the equation P = (d^(2/3) • s^3) / c.
Given:
d = 30,090 tons
s = 22.5 knots
c = 370
Substituting these values, we have:
P = (30,090^(2/3) • 22.5^3) / 370
Now, let's break down the calculations step by step:
1. Let's start with 30,090^(2/3):
To raise a number to the power of 2/3, you can take the square root of that number and then square the result. In this case:
30,090^(2/3) = (√30,090)^2
Using a calculator, we find that the square root of 30,090 is approximately 173.41.
So, (√30,090)^2 = 173.41^2
2. Next, let's calculate 22.5^3:
To raise a number to the power of 3, you need to multiply that number by itself twice. In this case:
22.5^3 = 22.5 x 22.5 x 22.5
Using a calculator, we find that 22.5^3 is approximately 11,390.625.
3. Now, let's substitute the calculated values into the equation:
P = (173.41^2 • 11,390.625) / 370
4. Let's evaluate the expression inside the parentheses:
173.41^2 = 30,073.9281
5. Now, let's calculate the numerator:
Numerator = 30,073.9281 • 11,390.625
Using a calculator, we find that the numerator is approximately 342,303,237.9.
6. Finally, let's divide the numerator by 370 to find the power needed:
P = 342,303,237.9 / 370
Using a calculator, we find that P is approximately 925,827.12.
Therefore, the ship needs approximately 925,827.12 horsepower.