**Housekeeping re: the 3.76616E-07 conversion factor.**
PeterE in post#14 suggested using the conversion formula from foot-pounds to kilowatt hours, in order to estimate the work required to "lift" a Bolt EV the amount of the

__vertical__ distance of the hill. Where, one (1) foot-pound (as a unit of work, not torque) equals 0.000000376616 kWh. XJ12 in post

#63 laid out how foot-pounds translate through standard international (metric) units in order to get to kilowatt hours.

Some debate ensued as to the useability of this ft-lb to kWh conversion. Whether or not it needed further adjustment for energy losses between the road wheel and the Bolt's battery. However, use of this 3.76616E-07 conversion gave surprisingly close results to test data (posts

#104 and

#105 ) from a Bolt 's readouts at the battery level. Now I know why.

After more investigation. CONCLUSION: the 3.76616E-07 conversion is accurate for estimating slope impact when measuring force

__at the road wheel __. But

__not __ as measured at the battery. The "proof" for this conclusion is detailed below. By way of matching the result of the 3.76616E-07 conversion, to the general formula for vehicle propulsion energy available from many authors. See bottom of this post for details. (caution: may cause headache).

Then the question becomes: what are the efficiencies (losses) from a Bolt's "battery to wheel" ? Absent someoneās live experiment, one way to estimate battery to wheel losses: compare the output of the "model" (see post

#137 ) which reasonably estimates kWh's used at the battery level for each mini-trip within a trip, both with and without the effect of slope. Compare that to: kWh's used at the road wheel as calculated from the general formula for vehicle propulsion energy, which is known to give the same result as applying the 3.76616E-07 conversion method.

Surprise: Bolt's battery to wheel loss as estimated this way, is only 5.2%* on average. Much much lower loss than was shown in post

#93 picture from the DoEās webpage. More in line with single digit loss that XJ12 referenced with some source information in post

#108 . (which I questioned, sorry

). Certainly this 5.2% battery to wheel loss estimate is wrong, but it might be a good indicator -- given available information it's quite likely that the % battery to wheel loss is a single digit one.

*- calculation performed using all Bolt parameters and quantified variables as based on uphill leg from Georgetown CO to Eisenhower tunnel entrance. Details are available.

What this means: the 3.76616E-07 conversion provides a quick way of determining incremental slope impact as measured at the road wheels. One can envision an elevation map digitized. Such as one sees when elevations pop out on Google Earth when manually running the cursor over each lat&long second on the map. The calculation of energy use due to hills becomes a piece of cake.

And given that the further adjustment required to derive kWh's at the Boltās battery, from kWh's at the wheel, is likely no more than 1.11 . It all forms a nice way of handling elevation changes. Which represent a very significant variable in predicting trip usage.

Great thread stanwagon. I learned a lot and had fun doing it.

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__ Proof: Conversion of foot-pounds directly to kWhās yields energy as measured at the road wheels __
Calculate the vehicle propulsion energy equation. (see post# 107 Van Sterkenburg, or other authors). Below example makes reference to trip leg assumptions using the grade above Georgetown CO to the Eisenhower tunnel. The assumed values for variables are not critical.

Energy required at the wheels for one second of time [

*Es*] is:

*Es = v*(Ā½*Cd*A*Ļ*v2 + m*g*(rw+sinĪø) + m'*a)*
where,

*v* ā planned speed in metres per second. assume constant speed going into the start marker, same constant speed over the leg and same constant speed departing the finish marker. assume 60 mph or 28.62 metres/sec.

*Cd* ā drag coefficient. 0.308 is latest published for Bolt EV.

*A* ā frontal area of Bolt in square metres. assume 2.816. (conservative, assume no air gap below frt spoiler)

* Ļ * ā density (weight) of air in kg. per cubic metre. assume 0.9 high altitude Colorado mountains.

*m* ā Boltās mass (weight GVW) in kilograms. assume 1707.8 or GVW of 3765 lbs one person + carryon.

*g* ā force of gravity in metres per second2 . assume standard 9.8.

*rw* ā rolling resistance coefficient. assume 0.0097881 for Bolt EV. estimate sourced

**here**.

*sinĪø* ā slope in radians. this hill is 3.54% or 2.03 degrees or .0354 radians. this hill begins at 9,211 feet and ends at 11,026 feet over a distance of 9.7 miles.

*a* ā acceleration

*a = āv / t *. in this example I've made

* a *zero by making

*āv *zero.

Other assumptions: ambient temperature 72F as embedded in parameters, assumption of no accessories usage - - no heat, no aircon, etc, (and probably some more assumptions that I havenāt thought of).

Result for 582 seconds and with slope = 0, is 6.943E+106 joules or 1.929 kWh.

Result for 582 seconds and with slope = 3.55% is 16.2112E+106 joules or 4.503 kWh (going uphill)

Delta due to slope is 4.503 minus 1.929 equals

__2.574 kWh.__ (A)
Now calculate the 3.76616E-07 conversion method.

Incremental work due to hill is

*āhlb * mlb * 3.76616E-07*.

Put in the values, (11026-9211)*3765*0.000000376616,

Result is

__2.574 kWh.__ (B)
(A) and (B ) are equal.