Hello, i tried to understand how the road dyno calculates the wheel power. I dont get the same reults as the dyno.
I gues the programm calculates from engine speed change per time the vehicle speed change per time wich would be the acceleration. With what Newton said F=m*a we can now calculate acceleration force. Multiplied with vehicle speed it gets acceleration power in kW. The power which works in opposite direction is roll- and air resistance which have to be added to the calc. acceleration power.
The problem i see is that i dont calculate same accleration as the dyno does. I have to know which dv/dt is used. I have table from log attached, grey cells are interpolated, i wonder that the rpm for calc peak power wasnt in the table, so i guess the dyno interpolated this rpm point. I interpolated the time at calc peak power an then i tried with interpolated values 500ms before and after peak power, i took this 1 sec period and calculated from engine speed change in this 1 sec the vehicle speed change, but i dont get exact same kW numbers as the dyno.
Another question i would have is which number the programm takes for air density.
Here my calc in detail:
From table attached(500ms before and after peak power):
∆n = 638,773 (1⁄min)/sek
gives:
∆v = (638,773 1/min * 2π * 0,31715 m)/(60 sec/min * 2,49 * 2,93) = 2,908 m/s
which ist vehicle speed change per sec = dv/dt = a = 2,908 m/s²
Wheel radius for 225/45R17:
r_Rad = 17''/2 *0,0254 m/zoll+0,225*0,45 m = 0,31715 m
with:
F = m*a
F_B = 1542kg*2,908 m/s^2 = 4483,914N
P_B = F_B*v
Now vehicle speed at peak power:
v = (n*2π*r_Rad)/(i_G*i_D )
v = (5645 1/min * 2π * 0,31715 m)/(60 sec/min * 2,49 * 2,93) = 25,698 m/s = 92,511 km/h
Accelerationpower P_B:
P_B = 4483,914 N*25,6998 m/s = 115,225 kW
Power against the car:
P_W = m*g*f_Ro*v+ρ/2*c_w*A*v^3
P_W = 1542kg*9,81 m/s^2 *0,012*25,698 m/s+((1,227 kg/m^3 )/2)*0,29*2,09m^2*( 25,698 m/s )^3
P_w = 10,975 kW
Wheelpower P_Rad:
P_Rad = P_B+P_W = 115,225 kW+10,975 kW = 126,2 kW
The difference is (126,8 - 126,2)kW = 0,6kW which is quiet close already.
Uncertainties are air density and acceleration.
My question is mainly if anybody knows how the dyno calculates the car acceleration?
EDIT: wrong dynograph attached
2nd-5th: I am very sorry i messed something up in the calculations.
