Engineering Explained: F-150 better than Cybertruck for towing duty (over distance)

[ajdelange]

The problem with your argument is that it assumes first that aerodynamic drag is dramatically less in the CT relative to other vehicles and second that aerodynamic drag is the dominant load on trailer and tractor. Were both of these assumptions valid then what you are saying would be true.

As I said in an earlier post the math is simple enough. The ratio of range with the trailer to range without is

r = 1/(f + 1)

where f is, in turn, the ratio of the sum of all the loads on the trailer (numerator) to the sum of all the loads on the tractor (denominator). The problem, as I said in my earlier post, is that of finding numbers to put into the sums. In the simple case where we tow a CT with another CT we might posit that the loads were the same on both in which case f = 1 and r = 1/2.

In the more interesting case (towing a loaded trailer) the job of finding f is complicated by the fact that there are several loads to consider
A)Drive train losses
B)Wheel slip losses
C)Drag
D)Rolling resistance
E)Gravity
F)Inertia
G)HVAC, headlights, windshield wipers...

Note that the trailer is not subject to A, B, or G loads. Also note that two of the loads, E and F can be negative numbers so that f can be negative and the range with a trailer can be larger than the range without. This could be the case for the lucky operator whose business involves trailering granite blocks from a quarry at the top of a mountain to a construction site in the valley. Thus r can assume any value between 0 and ∞.

The relative (that is, relative between type within tractor or trailer and between tractor and trailer) importance of loads depends not only on the design of the vehicles but on how they are operated. If you are in heavy traffic or in town the inertial load is probably the greatest. If you drive at constant speed on the freeway on level terrain the inertial load goes away (except for the initial acceleration). If you drive at low speed in town the drag load is most likely going to be insignificant relative to the slip and inertial loads. If you drive fast enough drag may become significant as it increases with the square of the speed. If you drive in hilly country the gravitational load will assume importance. As an example of this the average (winter/summer/day/night/hot/cold) load on my X is 301 Wh/mi. Driving on a 1% grade increases that by 108 Wh/mi.

Now when I see Elon promising extra goodies for trailering I get all excited because I realize that a simple load cell in the trailer hitch would allow the vehicle to compute the numerator in f and the display, which in the current vehicles, shows Wh/mi vs. distance traveled could now have a second trace showing the Wh/mi for the trailer alone. This would be a very powerful tool. Reviews of trailers could list the kWh the trailer will consume under various test conditions. Owners would soon learn the demands of their trailers just as they soon learn the demands of their cars now. Probably an engineer's midsummer's night dream but it could be pretty cool if they did that.

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[ajdelange]

https://www.electrictruckclub.com/post/expect-towing-to-kill-range-of-electric-pickup-trucks

As noted in the thread from which I pinched this the authors seem to be unaware that the inertial and gravity loads can assume dominance under some pretty common conditions.

 

[ajdelange]

I have to correct myself WRT drive train and slip losses. The trailer is subject to those because even though the trailer has no drive train or driven wheels its extra mass, drag and rolling resistance require more power of the motors in the tractor and thus increase those losses which, though they are dissipated in the tractor, must be entered on the trailer's side of the ledger. This correction only serves to illustrate further the complexity of the problem. The bad news is that it makes the job of accurate untangling of tractor and trailer loads based on a load cell in the hitch harder. My dream becomes a nightmare.

 

[Tribent]

I had a 2003 Dodge 3500 dually (with a 30 gallon tank) that I used to carry a 13000 lb 5th wheel all over the county. I usually kept my speed under 65 mph, and I would get around 10 mpg efficiency. That same truck would get around 24 mpg efficiency when driving the same speed without a trailer. Since the Cybertruck has better aerodynamics than the Dodge 3500, I would expect a larger drop in efficiency when hauling a trailer, but my point is that the efficiency drops off dramatically when hauling a trailer regardless of what you are using to haul it. I remember planning a fuel stop every 200 miles with that truck, so even though the range of the vehicle was well over 500 miles, it didn't get anywhere near that figure while hauling a trailer.

 

[ajdelange]

Since the Cybertruck has better aerodynamics than the Dodge 3500, I would expect a larger drop in efficiency when hauling a trailer,

A lot of people assume that but it isn't so to any dramatic extent and that's because the tractor's drag is a relatively small part of the motor load. Here is a list of loads that the motor(s) must satisfy:

1.)Tractor drive train loss
2.)Trailer drive train loss
3.)Tractor wheel slip loss
4.)Trailer wheel slip loss
5.)Tractor aerodynamic drag loss
6.)Trailer aerodynamic drag loss
7.)Tractor rolling resistance loss
8.)Trailer rolling resistance loss
9.)Tractor gravitational loss
10.)Trailer gravitational loss
11.)Tractor inertial loss
12.)Trailer inertial loss
13.)Tractor HVAC, lights, entertainment system...

As noted in an earlier post the trailer doesn't have a drive train nor any driven wheels so no drive train loss or slip loss occur on the trailer but as the tractor must pull harder and thus the motors produce more power with a trailer present the tractors drive train and slip loads go up when a trailer is present. Items 2 and 4 refer to those extra losses.

The range reduction (ratio of miles with to miles without the trailer) is:

r = (L1 + L3 + L5 + L7 + L9 + L11 + L13)/(L1 + L2 + L3 + L4 + L5 + L6+ L7 + L8 + L9 + L10 + L11 + L12 + L13)

in which each L represents the watt hours per mile required of the load corresponding to the index number. Do we really think a small change in L5 is going to have much of an influence on r? It will, of course, have some influence but given that there are so many other loads some of which swamp it, L5 isn't going to have much of an effect at all especially where one must speed up and slow down (the inertial load is really the elephant in the room) or when driving on positive grade. Most people (and that included me) don't appreciate that the slip load is a large load.

I had a 2003 Dodge 3500 dually (with a 30 gallon tank) that I used to carry a 13000 lb 5th wheel all over the county. I usually kept my speed under 65 mph, and I would get around 10 mpg efficiency. That same truck would get around 24 mpg efficiency when driving the same speed without a trailer.

For you r = 10/24 = 0.417. Now suppose you got from e-Bay a miracle spray which reduced the drag coefficient of your 3500 by 10%. Do you really think r would be much different from 0.417? If you pull this trailer over the same terrain driving in the same way you will find r for the CT will be about 0.417,

...but my point is that the efficiency drops off dramatically when hauling a trailer regardless of what you are using to haul it.

That's the important point!

I haven't been paying attention to the title of this thread: "Engineering Explained: F-150 better than Cybertruck for towing duty (over distance)". You can't say that something is better than something else without specifying what your definition of "better" is. If your definition is "tows farther with out having to refuel" then an ICE vehicle with a huge auxilliary tank is better. But if your definition is "tows a distance with reduced energy use" or "tows a distance at reduced cost" or "tows a distance with reduced emissions" then clearly a CT is better.

 

[Dids]

Let's discuss how power is developed and why a gas 150 would actually be more affected by towing than CT. Power is RPM and torque (force). In a gas ICE engine torque is low until significant RPM. To maintain that RPM over the constant minutia speed changes additional energy must be added. Mostly this is unnoticed as it is handled by the engine computer. The same is true with CT, if the RPM slows back emf reduces, current goes up. You really won't notice it happening but it is. Now electric motors have a very flat torque curve (the force to move is constant then starts dropping as motor is at operating speed due to back emf and forward emf + RPM balancing and current is at its lowest) If RPM drops current goes up and the motors torque goes up and RPM is maintained. For ICE if RPM drops fuel goes up but torque doesnt go up unless RPM goes up. If RPM cannot be maintained you have to downshift because adding more energy will not result in power. It is this change in the rate of energy added to maintain power over all the losses in the preceding post that is the biggest driver of range reduction.
How do you know this is true? Gas vs diesel. Deisel develops more torque at lower RPM and has a flatter curve. Therefore it is less affected by adding load than gas.
Electric motors are an even higher torque system with a better torque curve. It should be affected even less by load.

 

[ajdelange]

An ICE engine of either type is most efficient over a rather narrow range of rotational speeds thus we use gears or a CV transmission to keep it in that range or, in a diesel electric locomotive or marine application the engine is run at the best speed and used to turn a generator and the electricity from that generator runs electric traction motors. Electric motors (and note that I am not saying AC or DC as it is true of both) can independently control torque and flux at any speed and are, thus, efficient over a wide range of speed and load conditions thus preserving the efficiency of the prime mover. In a BEV the prime mover and generator are replaced by the battery,

In No. 61 I introduced the simplified formula

r = 1/(f + 1)

for the fraction of range achieved with a trailer as opposed to without one, In this formula f is the ratio of the loads of the trailer to the loads of tractor. Thus if the trailer introduces total load equal to that of the tractor f = 1 and r = 1/2. A more complete formula is

r = (1/(f+1)) * (1 - St)/(1 - Sv)

in which f is now the ratio of the sum of the trailer drag, rolling, inertial and gravity loads to the tractor's drag, rolling, inertial, and gravity loads. St is the slip when the trailer is being pulled and Sv is the slip when the tractor is not pulling the trailer. Note that with respect to No. 66 the slip factors are each multiplied by the motor efficiency which cancels out. Thus motor/engine efficiency is not a factor in range reduction and we expect the range reduction to be dependent on non-engine related parameters such as relative (tractor re trailer) drag coefficient, frontal area and weight - mostly weight.

 

[Cougs]

STUPID QUESTION:

Can this formula: r = (1/(f+1)) * (1 - St)/(1 - Sv) be used by Cybertruck software to continuously calculate the range while towing so that we can adjust speed, choose locations to stop and charge, etc....

 

[Dids]

STUPID QUESTION:

Can this formula: r = (1/(f+1)) * (1 - St)/(1 - Sv) be used by Cybertruck software to continuously calculate the range while towing so that we can adjust speed, choose locations to stop and charge, etc....

It is unnecessary. Any range calculator uses expended rate to forecast future rate via sliding average. The software already adjusts and shows you charge points based on that forecast.

 

[Cougs]

Thank you.

 

[Cougs]

I guess we need new formula other than lithium ion batteries that allows greater storage capacity (density), lighter weight batteries, or better solar capture cells that allows us to charge while driving or at least camping. I understand that this is a good start but science will break through. I hope soon???

 

[Dids]

I guess we need new formula other than lithium ion batteries that allows greater storage capacity (density), lighter weight batteries, or better solar capture cells that allows us to charge while driving or at least camping. I understand that this is a good start but science will break through. I hope soon???

Tesla battery day is coming in April. Meanwhile:
https://www.google.com/amp/s/www.cn...-buick-gmc-hummer-cadillac-electric-vehicles/

https://www.google.com/amp/s/mspowe...ct-roadrunner-game-changing-battery-tech/amp/

 

[Cougs]

It is all talk but no concrete results. They offered no specifics just talk. Those formulas discussed by GM will not offer any better range than what is available.

 

[ajdelange]

STUPID QUESTION:

Can this formula: r = (1/(f+1)) * (1 - St)/(1 - Sv) be used by Cybertruck software to continuously calculate the range while towing so that we can adjust speed, choose locations to stop and charge, etc....

Not stupid at all. Yes it can and, if they put a load cell in the towing hitch, do a much better job than the simple past mileage algorithms because it can estimate the load ratio for trailer and vehicle. Plus they can measure slip for truck plus trailer. The only part I am not certain about is how they would get Sv from measurement taken when the trailer is attached. Probably could be done by table look up from speed and acceleration.

Actually, as Tesla has all the internal data I'm sure they will come up with a more sophisticated formula/algorithm than this simple one.

 

[ajdelange]

I guess we need new formula other than lithium ion batteries that allows greater storage capacity (density), lighter weight batteries, or better solar capture cells that allows us to charge while driving or at least camping. I understand that this is a good start but science will break through. I hope soon???

Lithium ion covers a pretty wide spectrum with the lithium being incorporated in a variety of different salts at the cathode and with some variety in anode. In addition to that, performance depends greatly on electrolyte and electrolyte additives. They are not finished with Lithium by a long shot! I'm expecting that what we will hear on battery day is going to relate to new methods of manufacture (dry coating), variants in cathode chemistry (reduced cobalt, perhaps phosphate, silicon in the anode and perhaps new additives or maybe even a dry electrolyte but I think it's going to still be lithium all the way.

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