# So how many horsepower do you need

1. Oct 14, 2008

### mgb_phys

In a long drive home through the moutains I noticed that my car will do a constant 100km/h in gear with the engine running but no gas pedal down a 6% slope.

100Km/h = 27.8 m/s, in a 6% downgrade that's 1.7 m/s vertically.
kerb weight=1420Kg , so with 2 people and some fuel = 1600kg
mgh = 1600 * 9.8 * 1.7 J/s = 26Kw = 35bhp

So presumably cruising on the flat freeway at 100km/h I am also using 35bhp?
So why does the smallest engine I can buy in this car need 175bHp?

2. Oct 14, 2008

### foges

How about the power needed to accelerate to that velocity?

3. Oct 14, 2008

### gmax137

Or, how about the power needed to go up a hill? Or to burn rubber leaving the party? Also, you wouldn't want to be pushing peak power from your engine all of the time - it wouldn't last long before requiring a rebuild that way.

You're right though, the peak power is probably higher than it "needs" to be. That's one reason the easiest way to improve your fuel mileage is to drive more gently.

Edit - don't forget too, that if you are driving on the flats at your 100 km/hr, you are using that 35 bhp, you are not burning gas at a 175 bhp rate. What you are wasting is the fuel to overcome the mechanical (in)efficiency etc. of the bigger engine; and the extra weight associated with the engine, and heavier frame, and bigger brakes, and so on

4. Oct 14, 2008

### Naty1

If any environmentalists press you, tell them you have a bigger engine so you can do accelerometer studies.....don't mention impressing chicks!!

5. Oct 14, 2008

### mgb_phys

You know how people buy a Porsche or a 4x4 to make up for their small 'equipement'?
That's my 2cv over there ..wink.. ..wink..

6. Oct 14, 2008

### schroder

Well, are you sure that the smallest engine is 175 BHP? That sounds very high and I suspect it is the engine HP. BHP usually runs about 60% of engine HP and the manufacturers usually overrate the engine HP anyway. But, looking at the numbers you gave, since the car is not accelerating going down the grade, it must be at equilibrium between the friction forces and the x component of the Normal force. I calculate that as being 1640 N. That also seems a bit high so I suspect the engine and drive train are actually holding the car back, rather than helping to push it forward! In any case, let’s take that number and calculate the power at 27.8 m/s and we get 45600 Joules or about 60 BHP. So you need 60 BHP on the straight and level at 100 kph just to overcome friction forces. That corresponds to about a 100 HP engine. Now, if you ever want to do any accelerating up to the velocity of 100 kph, you will need about double force of 1640 N. Lets say 3200 N at 27.8 m/s which is 89000 J or 118 BHP. That corresponds to almost 200 engine HP which makes the 175 HP engine look a bit undersized. The cal’s are off a bit because we don’t have a good handle on the friction forces but I would say that 175 HP engine is about right for your car.

7. Oct 14, 2008

### mgb_phys

Yes 175hp is the sticker HorsePower, I wasn't aware of bhp/hp difference.
The car was rolling in gear but with no gas - so it's in equilibrium with gravity=aerodynamic + drive train drag. That was the experiment - the power needed to maintain 100km/h.

The result was interesting, my old Citroen probably had around 50hp and would get to 75mph/120Kmh (eventually). The new shiny car has permament 4wd which obviously adds a lot of drag (but it can REALLY accelerate = )