PCB Heaven
General Category => Maths, Geometry, Physics and others => Topic started by: colombo on September 15, 2008, 22:01:01 PM

A friend told me that he installed a new gadged on a ... rather expensive car (i will not mention brands). This gizmo, between all other measurements like tire pressure, speed etc etc etc, will also display the horse power that this car provides every time. Is this possible? Or is just a trick to make rich people happy and happy sellers richer?
col

The car itself may have an output that this thing uses the same protocol to get the data... A car like 5060K is not impossible to have one bus.

Maybe it's not the actual power, maybe it's the power generated by calculations and tests they had.

It is somehow possible to calculate it. You need to know some details of the car. I might be wrong after all but here is an idea:
We should distinguish the forces.
 First of all the force to move the car forward. I will call this F_{C}
 Also, the increment of the force when the car is climbing a hill. This i will call it F_{H}. To make things easier i suppose that we are not discussing for a rally Acropolis car and the driver will not step on the gas while going don the hill.
 The force to eliminate the air drag. This force i will call it F_{A} (and i found it from an auto test company)
 As for the turns, it is known that the friction is significantly increased and the efficiency of the motor and the gears to divide power is significantly decreased. But i will not calculate any of these. I will suppose that the driver is not stepping on the gas pedal when turning (safety first ;D)
Some parameters i will use:
V : The speed (velocity) of the car
g : 9.81 m/sec^{2}, the acceleration of gravity
M :The mass of the car in Kgs
q : The coefficient of rolling resistance. This is a typical value for new vehicles from 0.009 to 0.016
A : The surface of the front of the car that causes air drag in m^{2}
p : is the density of the air, approx 1.2 kg/m^{3} at sea level at normal temperatures
C : the Drag coefficient of the vehicles. A normal value is 0.36 to 0.39
s : The slope of the hill the car is climbing, in %
E : Energy
t : Time
Now to calculate these 3 forces:
Force to move the car forward. The car has to elimenate this force in order to move:
F_{C} = q x M x g
The increment of the force when the car is climbing a hill. This force will be added to F_{C}
F_{H} = s x M x g
The force to eliminate the air drag:
F_{A} = 1/2 x C x A x p x V^{2}
Our car has to generate enough power to elimenate all these drags. To calculate this power we should have in mind that:
(1) W = F x d that means Work = Force x distance
and
(2) P = W / t that means Power = Work / time.
(2) because of (1)becomes P = F x d / t
but (3) d/t = V so
(2) because of (3) becomes P = F x V
So:
P = F x V => Pol = (F_{C} + F_{H} + F_{A} ) x V
The above formula wil calculate the generated power for a given car at given speed in Watts. You may use the Power unit converter (http://pcbheaven.com/handbook/conversions/index.php?u=11) to convert this value to any other unit you want. But this will calculate the power for a car that is moving in constant speed straight or climbing a straight hill. Also, you must have in mind that all the forces that i added before must have the same direction!!!. So, if there is an air blow from the side of the car or the car is turning, you should calculate the Fol of each force.
In case the car is accelerating, you should use another formula t calculate the power generated as the speed is not constant.
First to calculate the energy:
E = 1/2 x M x V_{2}
And from the energy:
P = E / t, where t is the time needed to accelerate to a speed. The P is also in watts. use the Power unit converter (http://pcbheaven.com/handbook/conversions/index.php?u=11) to convert this value to any other unit you want.
So it comes that this gadget should have an accelerometer, a speed meter and a meter for the angle of the road to climb... It could be possible.

All this for that? Freaking car ;D

All this for that? Freaking car ;D
If you put it to work, it aint much. And it is more than exciting when you see theory in action.

Of course! ;D ;D ;D

Ok Ok, i believe you. You did some hocus pocus and you finally decide and prove that it can be done. I will take your word even if i do not understand a word from your words. But, with a simple GPS, one with no other things and sensors, is it possible? Please answer with a yes or no, and do not prove it ;D

Ya, sure, ok kam. You did it the hard way

Ya, sure, ok kam. You did it the hard way
The other way would be for the vehicle to be able to calculate to produced power according to rpm and throttle degrees of pressure and.... hmmmm..... i think... an idea comes to me. Let me think ::) ::) ::) ::) ::) ::) ::) ::) ::) ::) ::) ::) ::) ::)

What kind of idea exactly?

What kind of idea exactly?
Give me some time ;)

Very nice calculations!!!

Very nice calculations!!!
The magic in maths and physics is not when you make the calculation. The magic is that when you put them to work, if you have done them right, they work... That is magic

Ok Ok, i believe you. You did some hocus pocus and you finally decide and prove that it can be done. I will take your word even if i do not understand a word from your words. But, with a simple GPS, one with no other things and sensors, is it possible? Please answer with a yes or no, and do not prove it ;D
Hey people, you go over with your discussion of the subject i started and still did not get an answer. Please

YES
But don;t you wanna know how?