# Re: [EVDL] EVs and altitude?

```>From a Physics perspective, adding elevation increases your potential
energy (which comes out of the battery in an EV)
Which you gain back upon descent.
Formula: Ep = mgh
In Earth's gravitational field, near earth the g = 9.81
m is mass in kg
h is height in meters.```
```
So, using some random rounded numbers (fill in your own favorites and
repeat):
m = 2,000 (4400 lbs truck)
h = 300 (almost 1000 ft as was the question)
and let's assume it is a pickup truck, so it needs about 350 Wh per mi,
so 4 mi equates to 1.4 kWh of energy.

Ep = 2,000 x 9.81 x 300 ~ 6M (rounding 9.81 to 10 we get 6 million)
Joules.
One Joule is equivalent to one Watt-second.
So, one Watt-hour is 3600 Joules (since there are that many seconds in
an hour)
6M / 3600 = 1,667 Wh = 1.7 kWh

Indeed, an elevation gain of 1,000 ft (~300 meters) for a 4,400 lbs
truck costs at least as much energy as going 4 miles on flat road.
In fact, for the relatively heavy truck it is even over 5 miles.
For a lighter car, the amount of energy invested in elevation change
might be less.

NOTE that this energy is *on top of* the distance you'd need to drive to
get this elevation change.
So, if you take this truck, drive 3 miles to gain 1,000 ft then the
battery SoC would look as if you had done 3 + 5 = 8 miles.
And, you might need to account for higher losses in the components at
higher power level as well, but that is a secondary effect.

If you turn that truck around to go down 1,000 ft in 3 miles, the
battery will be re-charged with the difference between
The 3 miles you are driving and the 5 miles of range you are
recouperating from the height change, so your SoC should
Regain 3 + -5 = -2 miles. As a result, the SoC is showing the total of 8
+ -2 = 6 miles after driving 3 miles up and 3 miles down
And ending up at the same height as you started. Laws of Physics still
intact.
Hope this clarifies,
Cor.

-----Original Message-----
From: EV [mailto:ev-boun...@lists.evdl.org] On Behalf Of Robert Bruninga
via EV
Sent: Wednesday, May 03, 2017 8:06 PM
To: Electric Vehicle Discussion List
Subject: [EVDL] EVs and altitude?

I think I saw a reference that every 1000' climb in elevation is about
the same as 4 miles on level ground.  Is that the general rule of thumb
for EV's?

Bob, WB4APR
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