# Power and Tq Needed to keep a car rooling at speed

## Main Question or Discussion Point

Power and Tq Needed to keep a car rolling at speed

Ok so im working on a personal project to formulate hybrid systems for a given car.
Before i can do any of the electrical math however i need to find how much power and tq it takes to no only get the car moving but keep it moving (flat & any given degree of climb)

I found a site that shows me some basic stuff on how to find the forces acting on a car by the air at a given speed

a = Resistance from brake pads, or friction in the wheel bearings
b = Friction of the tires
c = Drag Coefficient
v = Velocity

The formula is great i'm sure..... BUT THEY DIDN'T GIVE ANY DAMN UNITS!!!!!
- some one help me please.
- How do you tie the Dc into every thing? I did some looking around and found a dc 0.31 for my car
- I also have no idea how to account for a car going up a slope, any one?
- How can i account for alt changes and temp changes? ( i think i need a simple formula for Pressure density)

I did find a quick and easy formula and found that i have about 446n acting on the front of the car at 120 kph or 75 mph. this in turns translates to ABOUT 16kw of power needed to keep the car at speed. what i'm wondering is where is this power applied. is this motor power? or just power needed at the wheel? i know from school that through gearing HP is divided by the gear ratio and Tq is multiplied by the gear ratio..... so how to i translate the 16kw it to Tq and HP at the Motor taking into account the tires?

Thank you for any help you guys/gals have to give. let me know if you need any other numbers.

just for Ref the car is a 05 Jetta TDI and weighs in at 3,300 lbs or 1,500 kgs

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Think i figured it out.

Ok so here is what i did.... (CHECK ME and let me know if i messed it up)
First i needed to find the force on my car. being that the force changes dynamically with the speed of the car.

I ran the car up to 85 mph and pushed in the clutch. Then I let it fall from 85 mph to 80 mph and started a timer. I then waited till it fell to 70 mph.

80 to 70 mph = 15 seconds
Avg Speed = 75 mph (121 kph)
Acceleration = .9778 f/s/s (.2980 m/s/s)

Knowing the acceleration from 80 to 70 mph i can then find the force acting on the front of the car

F = M*A

Mass of the Car = 3300 lbs or 1497 kg

F = 1497*.2980
F = 446 N

Power needed to Maintain 75mph (121 kph) = F * Av
Av = Avg speed (m/s) = 34 m/s

Power = 446 * 34

Power = 15,000 Watts (15 Kw) or 20 Hp

So from what i found it take 20 Hp to maintain 75 mph on flat ground (where i tested the forces on the car)

Now for the hills......

the Weight (force acting strait down) of my car:

1497kg * 9.8 m/s = 14671 N

For this i will use a 6% grade or 3.43 degs
the force traveling parallel to the road (pushing car back down the hill)

Fp = sin(deg) * Fd

Fp = Force parallel (N)
deg = 3.43
Fd = Force down or Weight (N)

Fp = sin(3.43)*14761

Fp = 878 N

By adding tFp to the force found on level road i think i came up with the force need to keep the car traveling at 75 mph up a 6% grade.

446 n +878 n = 1323.87 n

with the same speed (34 m/s) this comes out to and additional 30 kw or 40 hp for an over all need of 45 kw (60hp) to maintain 75 mph @ 6% grade with a 3300 lbs

So thats what "I" got let me know if i got this right.

just as a note. im about 3/4 throttle at 75 up a 6% slope (avg highway mtn pass here in Colorado) my car has 100 hp and 200 ft-lbs of tq. given some room for power loss do to the 9000 ft above sea level. 60 hp seams about right