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?
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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)
F_drag = 1/2 P V^2 C_DA = 0.5*0.002377*59^2*1555 = 6433 lbf
W = 3922000+150000+4451=4076451 lbs
7% grade = 4 degree
F_rolling= W*cos theta*Crr = 4076451*cos4*0.015=60998 lbf
F_weight=W *sin theta = 4076451*sin4=284359 lbf
F_sum = 6433+60998+284359=351790 lbf
P = F*V = 351790*59=20755610
hp = P/550 = 37737HP
3211.8 (3212)
Thank you!
except the answer of 3211.8 or even rounding up isn't one of the multiple choice options for the Dodge Challenge this week; I've whittled it down to 35 multiple choices and nothing even close this posed answer is amongst them
To calculate the horsepower needed to tow the SS Delphine up the Davis Dam Grade Climb, we will use the following formula:
F(sum) = F(drag) + F(rr) + F(weight)
Where:
F(drag) is the drag force
F(rr) is the rolling resistance force
F(weight) is the gravitational force
First, let's calculate the drag force (F(drag)):
F(drag) = 1/2 * p * V^2 * C(d)A
Given:
p (air density) = 0.002377 slugs/ft^3
V (velocity) = 40 mph (converted to ft/s: 40 * 1.467 = 58.68 ft/s)
C(d)A (combined coefficient of drag area) = 1555 ft^2
Substituting the values into the formula, we get:
F(drag) = 1/2 * 0.002377 * (58.68)^2 * 1555
Next, let's calculate the rolling resistance force (F(rr)):
F(rr) = W * cos(θ) * Crr
Given:
W (weight) = 3,922,000 + 150,000 + 4451 lbs (converted to slugs: (3,922,000 + 150,000 + 4451) / 32.174 = 127219.1 slugs)
θ (grade) = 7% (converted to radians: 7 * π / 180 = 0.122 radians)
Crr (coefficient of rolling resistance) = 0.015
Substituting the values into the formula, we get:
F(rr) = 127219.1 * cos(0.122) * 0.015
Finally, let's calculate the gravitational force (F(weight)):
F(weight) = W * sin(θ)
Substituting the values into the formula, we get:
F(weight) = 127219.1 * sin(0.122)
Now, we can calculate the sum of the forces (F(sum)):
F(sum) = F(drag) + F(rr) + F(weight)
Once we have the sum of forces, we can calculate the power required (P):
P = F(sum) * V
Lastly, we can convert the power to horsepower:
Horsepower = P / (550 ft lbf/sec)
By following these calculations, you can determine the horsepower needed for the Challenger SRT Hellcat Redeye Widebody to tow the SS Delphine up the Davis Dam Grade Climb according to the given parameters.