Why is brake mean eff.pressure higher at max.Torque than max.power?eqs

[marellasunny]

Why is brake mean eff.pressure higher at max.Torque than max.power?,I am looking for an explanation in terms of equations,since I already know the theoretical reason
i.e at Max.Power→the rpm is at Max for the engine →the friction losses are maximum→bmep at max power is lower than at max.torque.

$bmep=\frac{P_b(max)*n_R*10^3}{V_d*N}$

$\\ bmep(max)=\frac{6.28*n_R*T(max)}{V_d}$

the brake power definition does not in itself inculcate the friction losses,as you might well know,there exists another term 'friction power' for this purpose which does not even show-up in the above equations at all.So which part of the equations above suggest that the bmep being affected by friction?

 

[xxChrisxx]

Mean effective pressure is a non dimensional way of showing an engines capacity to do work per cycle independent of displacement. It is effectively a measure of how well the engine is breathing (ie how well the cylinders are being filled).

The engine has the most capacity for work when it is burning the most fuel, which occurs at peak torque. You may say that peak work comes at peak power, it is important to remember that this is per cycle, not per unit time.

The reason why peak torque and peak bmep occur at the same rpm is because the curves are the same shape. Take the bmep value relating to power and relating to torque:

n=2 for a 4 stroke engine

Pmep = Pn/VdN
Pmap = 2pi*Tn/Vd

If we lump together the constants. n and Vd and 2*pi we can see that Pmep is proportional to torque, but power still has an engine speed term.


We know friction is accounted for because it's a 'brake' value. Brake values are net output or measured values. 'Indicated' values do not take into account losses, the difference between the two values is the loss.

So in this case imep - fmep = bmep

 

[marellasunny]

I've got one more question,relating to volumetric efficiency for 4 valve eng. and 2 valve eng.
It is clear that Volumetric eff. is greater for 4 valve cylinders than 2 valve cylinders,since 4 valve cylinder input more air per cycle.But,how does one explain this in terms of a formula for volumetric efficiency?i.e Volumetric eff.=mass if air inducted per cycle per cylinder/density*Volume(rate) displaced by pist