cyberman
Well-Known Member
- First Name
- Nick
- Joined
- Mar 13, 2022
- Threads
- 3
- Messages
- 50
- Reaction score
- 32
- Location
- Preston, United Kingdom
- Vehicles
- 2022 Mustang Mach E AWD SR
- Occupation
- Retired
This isn't quite right. The force f holding back a vehicle, the so-called Road Load, is well known to be modelled accurately by a quadratic equation where the variable is the speed of the vehicle xdot:Energy required is proportional to the cube of the speed.
Regen is only helpful when it is being used in lieu of friction brakes. It is not responsible for better low speed efficiency.
Energy is measured in kWh, power in KW.
f road = a + b xdot + c xdotsquared + m g sin(theta)
where:
a is a constant and corresponds to the constant rolling resistance of the vehicle, especially the tyres;
b is a constant that corresponds to the velocity dependent rolling resistance;
c is a constant that corresponds to the air resistance of the vehicle;
m is the mass of the vehicle;
g is the force of gravity;
theta is the angle of the road surface with respect to the horizontal; on a flat road theta is zero and sin(theta) is zero meaning there is no change as a result of going uphill or downhill.
So, the Road Load is a little dependent on vehicle speed through b and strongly dependent on the speed squared through c. It's this drag on the vehicle proportional to speed squared that kills the efficiency of any vehicle as the speed increases.
For my own interest I recently put together a spreadsheet of this equation for my Mach E AWD with Standard Range battery:
Road Power Load calculation | ||||||
g = | 9.81 | m / s2 | ||||
f road = | a + b xdot + c xdotsquared + m g sin(theta) | |||||
Coefficients | Kinetic energy = | 1/2 m xdotsquared | ||||
a | 31.9 | lbf | ||||
b | 0.3973 | lbf/mph | ||||
c | 0.01956 | lbf/mph**2 | ||||
Vehicle mass | ||||||
AWD SR | 2640 | kg | ||||
Driver | 67 | kg | ||||
1 lbf is equal to: | 4.4482216 | N | ||||
Speed, xdot | mph | m / s | F road / lbf | F road / N | P road / W | P road / kW |
0 | 0 | 31.9 | 142 | 0 | 0.0 | |
10 | 4.470272687 | 37.829 | 168 | 752 | 0.8 | |
20 | 8.940545373 | 47.67 | 212 | 1896 | 1.9 | |
30 | 13.41081806 | 61.423 | 273 | 3664 | 3.7 | |
40 | 17.88109075 | 79.088 | 352 | 6291 | 6.3 | |
50 | 22.35136343 | 100.665 | 448 | 10008 | 10.0 | |
60 | 26.82163612 | 126.154 | 561 | 15051 | 15.1 | |
70 | 31.29190881 | 155.555 | 692 | 21652 | 21.7 | |
80 | 35.76218149 | 188.868 | 840 | 30045 | 30.0 | |
90 | 40.23245418 | 226.093 | 1006 | 40462 | 40.5 | |
100 | 44.70272687 | 267.23 | 1189 | 53138 | 53.1 | |
110 | 49.17299955 | 312.279 | 1389 | 68306 | 68.3 |
There are lots of observations that can be made from the numbers and the graph. Here are just a few:
1. The numbers are all rather low down at 10 or 20 mph. This is just the rolling resistance of the vehicle.
2. The Road Load at 50 mph is 10 kW but at 70 mph it is twice that: 21.7 kW
3. At 100 mph the Road Load is more than 5x its value at 50 mph. Don't expect much range if you drive at 100 mph!
I hope some of the above is helpful. It's not an exact simulation but it does use real numbers for the Mach E AWD SR taken from a dynamometer (I think).
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