Question

Even, in 1921, the Dodge Brothers built a boat named the SS Delphine and it had a whopping 3000 HP. 

So, how much horsepower would a Challenger SRT® Hellcat Redeye Widebody need to tow the SS Delphine up the industry standard: Davis Dam Grade Climb?

Pro Tips

Davis Dam assumed grade = 7%

Air density is sea level conditions (.002377 slugs/f^t3)

w(weight) of the SS Delphine + trailer + Redeye = 3,922,000 + 150,000 + 4451 Lbs

Crr = coefficient of rolling resistance = .015

Assume Combined CDA is 1555 ft^2

SAE J2807 (Davis Dam Grande Climb) - min speed is 40mpg (59 ft/s)

F(drag) = 1/2p x V^2 x C(d)A

F(rolling resistance) = W x cos x Crr

F(weight) = W x sin

F(sum) = F(drag) + F(rr) + F(weight)

P = F(sum)XV

convert to horsepower = P(1hp/550ft lbf/sec)

Answer 1

The answer can be obtained by direct substitution of the values into the formula

7% grade = 4 degrees

Total weight (W) = weight of the SS Delphine + trailer + Redeye = 3,922,000 + 150,000 + 4451 Lbs

= 4076451 lbs

Minimum velocity to climb = 59 ft/s

Net drag experienced = rolling friction + vertical pull of the gravity + Drag (due to the wind turbulence)

Rolling friction = W x cos(4) x Crr

Crr = coefficient of rolling resistance = .015

Rolling friction = 4076451 X cos4 X 0.015

= 60998 lbf

vertical pull of the gravity = W X sin4 = 4076451 X sin4

= 284359 lbf

Drag = 1/2 X p X V^2 X C(d)A

= 0.5 X 0.002377 X 59² X 1555

= 6433 lbf

Net drag = 6433+60998+284359

= 351790 lbf

Minimum power required = P = F X V

V = minimum speed = 59 ft/s

P = 351790 X 59 = 20755610 ft lbf/sec

Converting it into horse power,

hp = P X (1/550) hp

horse power = 20755610 X (1/550) hp

horse power = 37737 hp