How much horsepower would a vehicle need to run the speed of sound arrive before the sound of its engine arrives?
Assume vehicle weighs 4492
Assume no wind
Assume no driveline losses
Vehicle traveling at sound of speed (760 MPH = 1116.4ft/sec)
What you need to know:
HP = Fsum x V/hp
F drag = 1/2 pv^2 CdA
F rolling resistance = Crr x weight
F sum = F drag + F rolling resistance
Cd = .398
A = 26.72 Ft^2
Crr = .015
p= .002377 slugs/ft^3
You didn’t solve for P
P=.002377 x 141.1 / ft^3
This is so wrong, there are so many Missing units. Your not winning this week Jay. If you know you know. Better luck next week
To calculate the horsepower required for a vehicle to reach the speed of sound before the sound of its engine arrives, you need to consider the drag force and rolling resistance force acting on the vehicle.
1. Find the drag force:
The drag force can be calculated using the formula: Fdrag = 0.5 * p * v^2 * CdA
where:
- Fdrag is the drag force
- p is the air density (approximately 0.002377 slugs/ft^3)
- v is the velocity of the vehicle (in this case, the speed of sound, which is approximately 1116.4 ft/sec)
- Cd is the drag coefficient (approximately 0.398)
- A is the frontal area of the vehicle (approximately 26.72 ft^2)
2. Find the rolling resistance force:
The rolling resistance force can be calculated using the formula: Frr = Crr * weight
where:
- Frr is the rolling resistance force
- Crr is the rolling resistance coefficient (approximately 0.015)
- weight is the weight of the vehicle (in this case, assumed to be 4492 lbs)
3. Find the total force on the vehicle:
The sum of the drag force and rolling resistance force will give you the total force: Fsum = Fdrag + Frr
4. Calculate the horsepower:
The horsepower required can be calculated using the formula: HP = Fsum * v / hp
where:
- HP is the horsepower required
- Fsum is the total force on the vehicle calculated in the previous step
- v is the velocity of the vehicle (in this case, the speed of sound, which is approximately 1116.4 ft/sec)
- hp is the conversion factor of force to horsepower (1 horsepower is equal to 550 ft-lbf/sec)
By plugging in the values into the formulas, you will be able to calculate the horsepower required for the vehicle to reach the speed of sound before the sound of its engine arrives.
I mean the slugs equal 138.4261 if the curb weight is 4451
Assume vehicle weighs 4451
F rolling = 0.015 x 4451 = 66.765
F drag = .398 x 26.72 x .5 x .002377 x 1116.4^2 = 15752.82
F sum = 66.765 + 15752.82 = 15819.59
HP = 15819.59 x (1116.4/797) = 22159.33
Vehicle would need 22159.33 horsepower to travel speed of sound!