[SGVLUG] OT: Hybrid efficiency (was:New Linux Lug)

[David Lawyer]

On Mon, Feb 20, 2006 at 08:00:35PM -0800, Dustin Laurence wrote:
> On Mon, Feb 20, 2006 at 03:59:35PM -0800, David Lawyer wrote:
> 
> > Of course it saves fuel.
> 
> Note specifically that I believe it is *not* the kind of driving you
> advocated.  You were talking about big speed changes, which guarantees
> lots of extra drag at the same average speed.  Since I happen to
> remember how the drag works, I know very well that's a loss in drag
> terms.

You're of course right if we require the same avenge speed.  But as a
practical matter, one can't use long coasting periods and maintain the
same average speed without significantly exceeding the speed limit.
So I'm comparing apples and oranges in a sense.

> 
> Also it's odd how you seem to think this but don't understand the
> advantages of a pure hybrid being always able to run it's engine at the
> most efficient place.  A hybrid sort of does what you're trying to do
> here, the difference is it does it better, more safely, and without
> abusing the machinery.
Again, inspect the curves and you'll find that it is nearly as
efficient to operate at widely varying rpm.  Running at near max
torque and then coasting doesn't abuse the machinery.  The engine
and drivetrain are designed to run at max torque.  Sure, there is
more cyclic fatigue on the drive train, but are you aware that steel
(as contrasted with aluminum) has a fatigue limit.  After a large
number of cycles, there is no more fatigue.
> 
> > As for wind resistance, you'll get better efficiency with long pulses,

I'm not comparing them at the same average speed.  No need for me to
read your derivation since I'm well aware of this principle.
> 
[snip]
> The point is, what does save gas is essentially pumping the gas pedal
> rapidly, so that the speed changes very little.  Which is what I said,
> and different than your scenario where v = 2u, which loses

The problem with doing it rapidly is the loss of and angular momentum
of the engine and the need to create this momentum again when starting
up the engine.  All this is energy wasted.  So long coasting phases
reduce this waste.

Thanks for discussing this with me.  I think I'll write an article
named "The Case for Coasting" and explain this better.  I can't just
say to recover KE by coasting without explaining it in detail.

Actually I should include mathematical arguments based on optimal
control theory using the calculus of variations:
You write down the differential equations of motion:
dx/dt = v
dv/dt = u(t) - r(v) - g(x) 
Where
u = force per unit mass applied at the driving tire tread
r = vehicle resistance in force per unit mass (specific drag)
g = grade resistance

We need to find the optimal control u(t) and the final time T so as to
minimize the cost function:
Integral wrt/time { v*u*e[i] + d } limits: 0,T where:
Initial conditions: x=0 and v=0; at t=0	
Final conditions x=L and v=0; at t=T
u(t) is constrained between a max and min (depends on v)
e[i] = cost of mechanical energy at the tire.
i=1 when u > 0 (powering)
i=2 when u < 0  and regenerative braking
i=3 when u < 0 and mechanical braking
Note e[1] > e[2] > e[3]; only e[3] < 0 
d = The cost of time.  (If there were no cost of time, T (the final
time T) would be infinite.

Note that this problem represents a trip between two points with no
stops in between (and no speed limits).  I formulated it for the case
of electric railroad trains that can regenerate energy.

Finding the optimal control u(t) will result in an optimal trajectory
x(t) and v(t).  To do this is a standard problem in control theory.
The optimal solution shows that a coasting phase (with u=o for a
non-zero amount of time) is always part of the optimal solution)>

So it implies that hybrids need to coast too in order to improve their
efficiency.  A hybrid using coasting polices would perhaps be more
energy-efficient than a non-hybrid using coating policies.  The
question then remains: Would it same enough energy to justify the
increased cost of the hybrid?

			David Lawyer