Santa's sleigh currently runs at 203mph, but he needs it to reach 400mph with all the packages he has to deliver.
If Santa is delivering presents at an altitude of 5,813.6ft, with the same drag and weight of a 2019 Challenger SRT hellcat redeye, how much HP would he need to reach 400 mph?
Tips:
100% driveline efficiency
P (air density) at 5813.6 ft = .0019 slug/ft^3
A (Area of Challenger front end) = 26.72 ft^2
C(d) (Coefficient of drag) = .398
Goldberg's sleigh required speed, 400 MPH = 587 ft/sec
F(drag) = 1/2 p x v^2 x C(d)A
P = F(drag) x V
Convert to Horsepower = P ( 1HP/550 ft lbf/sec)
0.5 x 0.0019 x sqr(587) x 0.398 x 26.72 = 3,481.12
3481.12 x 587 = 2,043,419.03
2,043,419.03 / 550 = 3715
you're welcome!
3715 hp
3700 hp
He flies at 7,200 mph according to my math not reflected by this equation.
To calculate the horsepower Santa would need to reach 400 mph with his sleigh, we can use the formula:
P = F(drag) x V, where P is the power (in horsepower), F(drag) is the drag force, and V is the velocity.
First, let's calculate the drag force using the formula:
F(drag) = 0.5 x P x v^2 x C(d) x A, where P is the air density, v is the velocity, C(d) is the coefficient of drag, and A is the frontal area.
Given information:
P = 0.0019 slug/ft^3 (air density at 5813.6 ft)
v = 587 ft/sec (the required speed of 400 mph converted to ft/sec)
C(d) = 0.398 (coefficient of drag)
A = 26.72 ft^2 (frontal area of the Challenger)
Let's calculate the drag force:
F(drag) = 0.5 x 0.0019 x 587^2 x 0.398 x 26.72
Now, let's calculate the power (in horsepower):
P = F(drag) x v
Finally, let's convert the power to horsepower:
1 horsepower = 550 ft lbf/sec
So, the final step is to divide the power by 550:
P (in horsepower) / 550
By following these steps and plugging in the given values, you can calculate the horsepower Santa would need for his sleigh to reach 400 mph.