Air density @ sea level, 59 degrees, no wind = p = .002377 slugs/ft^3
Coefficient of drag (flat plate, NASA) = C(d) = 1.28
Weight = W = 4451 lbs
Gravitation constant = g = 32.2 ft/sec^2
Area = A = 197.5" long x 78.2" wide x (1 ft^2/ 144 in^2)
Vehicle falls flat, wheels 1st, straight down, at constant acceleration with no aerodynamic drag until terminal velocity
Horsepower needed to accelerate is AVERAGE - not peak
100% driveline efficiency
To calculate the horsepower needed to accelerate a vehicle falling flat, wheels first, straight down, at a constant acceleration with no aerodynamic drag until terminal velocity, we need to consider the weight of the vehicle, the drag force acting on it, and the acceleration.
1. Calculate the mass of the vehicle:
Mass (m) = Weight (W) / Gravitation constant (g)
Given: Weight (W) = 4451 lbs, Gravitation constant (g) = 32.2 ft/sec^2
Convert weight to slugs:
Weight (W) = 4451 lbs * (1 slug / 32.2 ft/sec^2) = 138.2907 slugs
2. Calculate the drag force:
Drag force (F(d)) = 0.5 * Air density (p) * Coefficient of drag (C(d)) * Velocity^2 * Area
Given: Air density (p) = 0.002377 slugs/ft^3, Coefficient of drag (C(d)) = 1.28, Velocity (V) = Terminal velocity (assumed), Area (A) = 197.5" * 78.2" * (1 ft^2/144 in^2)
Convert area to ft^2:
Area (A) = (197.5" * 78.2") / 144 = 107.5965 ft^2
3. Calculate the terminal velocity:
Terminal velocity (Vt) is the speed at which the acceleration becomes zero, and the drag force matches the weight of the vehicle.
When F(d) = W, we can solve for Vt:
0.5 * p * C(d) * Vt^2 * A = W
Vt = sqrt((2 * W) / (p * C(d) * A))
Substitute the given values:
Vt = sqrt((2 * 138.2907 slugs) / (0.002377 slugs/ft^3 * 1.28 * 107.5965 ft^2))
4. Calculate the horsepower needed to accelerate:
Horsepower (HP) = (Drag force * Velocity) / 550
Given: 100% driveline efficiency
Convert velocity to ft/sec:
Velocity = Terminal velocity (Vt) * (ft/sec)
Substitute the given values:
HP = (F(d) * Vt * ft/sec) / 550
Now you can plug in the calculated values into the above formula to find the horsepower needed to accelerate the vehicle falling flat, wheels first, straight down, at a constant acceleration with no aerodynamic drag until terminal velocity.