Optimum EV cruise speed musings?

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Optimum EV cruise speed musings?

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I saw that the optimum range EV speed for the Volt is about 37 MPH.
This comes from the fact that there are constant battery loads (200 Watts)
Gearing which sets the optimum efficiency of the motor at a given speed.
Then increasing drag proportional to speed (road friction).
And then the increasing air drag (cubed) due to air speed.

Lets say they all combine to give that 37 MPH optimum max range speed for
the Volt.

Now the question.  When one is going up a mild hill (gaining altitude) or
generally almost coasting going down the mild hill, then the optimum point
must clearly have moved a bit.  Which way?

If 37 MPH on the level gives max range, should I increase a bit or
decrease speed a bit going up a hill?  Here is my thinking...

1) The potential energy gained/lost is linear with altitude and not
affected by speed, so that is a wash.
2) The fixed losses remain constant
3) Then Air and road drag are proportional to speed.
4) But motor "load" is proportional to the altitude changes.

So the best I can come up with is that any change in optimum speed going
up or down a hill is mostly related to the small constant fixed losses.  A
good analogy in a gas car is that you are driving with a pinhole in the
tank.  You are losing gas no matter what you do, so the faster you go, the
less gas simply lost through the pinhole when you arrive at destination.*

So when coasting down a  hill and the motor is using way below optimum
energy, then I think it makes sense to add a few MPH to bring the speed
losses up to again re-balance against the fixed losses.

Conversly, when going  up a hill, and the motor losses due to altitude are
greater, then it makes some sense to slow down a tad to again, rebalance
the added load of altitude against the fixed losses.

I'd love to see the equations and solve for the magic MPH compensations
for hillls.  Of course it is dependent on the slope.

Could it be as simple as watching the AMPS gauge and when going up a hill
reduce speed until the amps get back down to cruise amps, and going down a
hill increase speed to make the amps equal the cruise amps.  I DON'T THINK
SO.  The slower speed going up hill would be too slow and down hill you'd
kill yourself.

Ah Ha!  I think the answer is not comparing to Cruise AMPS, but only the
portion of the cruise amps that are due to speed, and not all the other
components of those amps.   Hummh...

One other factoid.  The energy per mile is generally assumed to be about
250 Whrs per mile.  And if the car is just sitting there and not moving,
then that is the same as driving at 1 MPH.  A trivial difference.  BUT,
the typical 250 Whrs per mile quoted is really an overall value at normal
driving speeds.  SO it is surely greater at lower speeds.  Maybe all I
need to do is just sit in a flat parking lot, release the brakes and just
see how fast the car arrives at while sill only consuming the fixed 0.5

Hummh anyone done this?

Bob, Wb4APR

* the asterix is from a fighter pilot who remembers looking out the window
on takeoff after getting a repaired gas tank.  His copilot said "we are
losing fuel!!! By the gallons!".  Pilot rammed the stick to afterburners
for MAX power to get back and land ASAP.  This is counter intuitive.  Many
would go into limp mode to conserve fuel to get back to landing.  WRONG.
TO quote the pilot "I was losing hundreds of pounds of fuel per minute and
I wanted to make sure what fuel I had left was all going through  the
engine and not out the open hole."... RIGHT decision.
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