If we recreated the scene from Fast & Furious 7 and dropped a Challenger SRT® Hellcat Redeye Widebody from a C-130 aircraft at 5,280 ft, how much horsepower would it take to drive past it before it hits the ground if you’re 1 mile away?
- 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
Vt=sqrt((2x4451)(0.002377X1.28x107.4))
107.4 is the product of (197.5 x 78.2) / 144 to find the sq ft of the car
vt=sqrt(27225)=165
tvt=165/32.2
dvt=.5X32.2X5.12^2=422
dr=5280-422=4858
tr=4858/165=29.4
aavg=2(5280)/(34.4^2)=8.87
p=((4451/32.2)X8.87X5280)/34
p=190405
hp=p/550=190405/550=346 rounding error so answer is 341 for the challenge
1221 is not correct. The answer should be 341
9850 HP
To calculate the horsepower needed to drive past the falling Challenger SRT Hellcat Redeye Widebody before it hits the ground, we need to consider a few factors.
First, we need to determine the time it takes for the car to fall to the ground from a height of 5,280 ft (1 mile). Since we know the acceleration due to gravity is 32.2 ft/sec^2, we can use the formula for free fall:
Time = sqrt(2 * height / g)
where height is 5,280 ft and g is 32.2 ft/sec^2.
Next, we need to calculate the terminal velocity of the Challenger SRT Hellcat Redeye Widebody. Terminal velocity is the maximum velocity an object can reach when the force of gravity pulling it downward is balanced by the air resistance pushing against it. We'll assume there is no aerodynamic drag until the car reaches terminal velocity.
The drag force can be calculated using the formula:
Drag Force = 0.5 * p * A * C(d) * V^2
where p is the air density at sea level (given as 0.002377 slugs/ft^3), A is the area of the car (197.5" long x 78.2" wide converted to ft^2), C(d) is the coefficient of drag (given as 1.28), and V is the velocity.
At terminal velocity, the drag force equals the weight of the car, which allows us to solve for the terminal velocity using the formula:
W = Drag Force
where W is the weight of the car (given as 4451 lbs).
Once we have the terminal velocity, we can calculate the distance the car would fall in the time it takes to reach the ground. We'll assume the car falls with constant velocity after reaching terminal velocity.
Lastly, since we know the distance between the starting point and the landing point (1 mile), we can determine the velocity at which the car needs to travel to cover that distance before it hits the ground.
To calculate the horsepower needed, we need to convert velocity from ft/sec to miles per hour and then use the formula:
Horsepower = (force * velocity) / 550
where force is the weight of the car (in pounds) and velocity is in miles per hour.
By following these calculations, you can determine the amount of horsepower needed to drive past the falling Challenger SRT Hellcat Redeye Widebody 1 mile away before it hits the ground.