Range reduction when towing.

[ajdelange]

It'll take the same amount of energy to move the trailer whether BEV or ICE if I understand correctly.

I wanted to keep #30 as simple as possible and so didn't comment on this. In fact it takes less energy to move the trailer with a BEV than with an ICE vehicle because some of the energy that goes to the trailer when it is towed by and ICE vehicle gets converted to heat in the trailers friction brakes. In an ideally executed tow with a BEV the brakes are never used and in a less than ideal situation are used less than they are than they would be with the ICE vehicle. IOW regen reduces the energy used by the trailer and it reduces the energy used by the truck. Based on #30 the reduction fraction is
1/(1 + T/V)
in which T is the energy demand of the trailer and V the energy demand of the vehicle towing it. For a simple analysis we might assume that regen reduces those by the same factor, call it f. Then
1/(1 + f*T/f*V)
and we see that f cancels so the reduction is the same though regen clearly saves us total energy so while the reduction is smaller the distance we can go is longer. For example, the CT will give us 500 mi EPA with regen, Using the numbers from #30 we'd expect to see that reduced t0 0.4*500 = 200 with the trailer. Without regen the unburdened range might go down to 450 miles and with the trailer we would then expect to see 0.4 * 450 = 180 mi,

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[TyPope]

In an ideally executed tow with a BEV the brakes are never used and in a less than ideal situation are used less than they are than they would be with the ICE vehicle.

Just wanted to check on that "only quote the part you are commenting on" thing.

If your trailer brakes aren't used, you can easily get into a horrible porpoising event where the trailer whips back and forth. It's what put my Wife head-first into the guardrail (she and the girls were fine). It is also from my first lesson on the subject from my Dad as we were pulling a trailer loaded down with sheets of wood to redo our roof with no trailer brakes. We were going about 25 mph when the whipping started and my dad showed me that you have to accelerate to stop it if you don't have trailer brakes. The car couldn't accelerate due to it being a Plymouth Reliant and weak as all get out... I remember that even at 5mph, that trailer was still lurching back and forth. The wood stack was now about a foot further back in the trailer than it had started and the rest of the 5 miles home was VERY slow. You have to have trailer brakes and standard brakes will lose energy through heat unfortunately. No, the best thing would be a trailer with at least a single motor and small battery pack to help offset losses. In my opinion.

 

[ajdelange]

If your trailer brakes aren't used, you can easily get into a horrible porpoising event where the trailer whips back and forth.

You are describing "sway". Porpoising is a motion in the vertical plane similar to phugoid oscillation in an aircraft or the way a porpoise cruises.

It's what put my Wife head-first into the guardrail (she and the girls were fine). It is also from my first lesson on the subject from my Dad as we were pulling a trailer loaded down with sheets of wood to redo our roof with no trailer brakes. We were going about 25 mph when the whipping started and my dad showed me that you have to accelerate to stop it if you don't have trailer brakes.

Yes, there is little doubt that trailer sway is a nasty business and there have been lots of accidents caused by it especially since the driver's reaction to it is often such that the amplitude of the oscillation increases (trailer swings to right rotating vehicle nose to the left, driver reacts by steering sharply to right whipping trailer left, trailer swings left ...). Steering straight and accelerating or applying trailer brakes are both solutions that apply a torque in the correct direction to reduce the sway and get the trailer back in line.

Now we are talking CT here. The trailering CT model is the TriMotor and it has independent motors on the rear wheels exactly where the counter torque needs to be applied. Plus it has rotation and inertial sensors and, given some of Elon's promises, strain gauges in the hitch and the computing power to sense impending sway and correct for it. Thus I expect that the CT with a trailer is going to be a lot more resistant to sway than a conventional vehicle. Trailers will still be equipped with brakes, of course and thus there will be brake controllers and those controllers will still have the manual lever but I believe the trailer brake will be used less from pedal input and, we hope, never from lever input and that, thus there will be a reduction in the amount of energy wasted in the trailer by friction braking just as there will be in the CT itself.

 

[TyPope]

You are describing "sway". Porpoising is a motion in the vertical plane similar to phugoid oscillation in an aircraft or the way a porpoise cruises.

You are correct. I don't know why I used porpoising in that explanation. Wasn't thinking. I get that the CT will be able to counter trailer sway just like any vehicle made now can with their brakes. My wife's car also had anti-sway control AND an anti-sway bar installed. But, all that does is hide the real problem until it exceeds the system's capability to manage it at which point, even though she locked the trailer brakes as hard as she could (using the pinch control) and then tried accelerating through the sway like I taught her, it was too little, too late. Bam! Car parts everywhere. We now know that the trailer brake was set too loose and that did not enable the trailer to drag behind the Expedition rather than just push it down the steep decline we started. It was also a little icy there.

Anyway, we definitely need some kind of trailer brake control built in and I'm sure Tesla does that already and will definitely have that capability in the CT. What would be neat is if we can utilize the trailer "brakes" to regen. You just can't have the trailer shoving the car towards a red light. So, the trailer needs to lead that braking effort a bit... perhaps through some regen action.

 

[ldjessee]

All models of the CyberTruck have decent towing capacity and with the middle trim having a 10,000lb towing capacity, not sure how the TriMotor is the 'towing' version.

Sway will need to be dealt with by all CyberTruck models.

 

[ajdelange]

You are correct. I don't know why I used porpoising in that explanation.

Probably because lots of other people do.

Anyway, we definitely need some kind of trailer brake control built in and I'm sure Tesla does that already and will definitely have that capability in the CT.

No, they don't. They have connectors into which one can plug a trailer brake controller but no internal brake controller. And I'm guessing they won't unless they build their own trailer and here's why. If they stay the way they are and you go buy a trailer and a controller for it (or not) the onus of making sure that you have a safe trailering setup is entirely on you and maybe somewhat on the third party that makes the brake controller.But definitely not Tesla.

What would be neat is if we can utilize the trailer "brakes" to regen.

Yes it would but that would mean motors and controllers on board the trailer that interface with the control system in the CT and the BMS. That obviously is not going to happen with a third party trailer. But who knows whether Tesla will ever make trailers. These considerations obviously apply to the Semi too. The Semi would get more range if it can be dynamically braked with the energy recovered going to the tractor than it could with air brakes.

You just can't have the trailer shoving the car towards a red light.

Sit down before reading this next sentence. That's exactly what you have every time you see a U-haul. Some boat trailers have an arrangement whereby the hitch pushes back on a hydraulic piston thus applying braking automatically. I guess that works to some extent.

So, the trailer needs to lead that braking effort a bit... perhaps through some regen action.

Some of the controllers have a a pendulum. If you as much as take your foot off the gas you start to slow down and the pendulum moves forward (in the vehicle frame). This sends a signal to the trailer brakes. This obviously causes loss that could be recovered if the torque vectoring can control the sway danger up to some point. Clearly there is some systems engineering that needs to be done.

 

[ajdelange]

All models of the CyberTruck have decent towing capacity and with the middle trim having a 10,000lb towing capacity, not sure how the TriMotor is the 'towing' version.

Engineers spend careers looking at design trades and eventually develop a sort of sixth sense as to what a designer might have had in mind. Of course the conclusions are based on sixth sense, but not fact so the conclusions drawn can be off. But the numbers for the CT strongly suggest that towing was the driver in the TriMotor design.:

There are some guesses and assumptions that went into this, of course, such as the CT weights. The assumption was made that 0 - 60 times are based on uniform acceleration and that the maximum thrust available is that required to produce that acceleration and that the maxium power is that at the 60 mpH end of that acceleration. Only kinetic energy increase was included in the calculations.

Thus the Trimotor will pull almost twice as much weight twice as far as the RWD and get it up to 60 mph 1.6 times faster. Mutiplying these factors together (and you can, of course, argue that there is a better FOM and perhaps there is) makes the Trimotor 5.9 times better at towing than the RWD and twice as good as the AWD.

Oops. I forgot to include torque vectoring DOF in this. I give each friction brake half a DOF (because it can only induce drag) and each motor one because it can induce drag and thrust. Adding the DOF factor to the FOM the Trimotor is 9.9 times better than the RWD and 2.5 times better than the AWD.

Sway will need to be dealt with by all CyberTruck models.

Sway will have to be dealt with by all CT model drivers. About all Tesla does now when a trailer is sensed is turn off certrain autopilot features. But Elon has promised new trailering features in the CT. It will be interesting to see what the lawyers will let him do. Certainly the large number of torque vectoring DOF in the Trimotor design lend lots of opportunities here.

 

[Newton]

I really like this rundown, good job Jim.

but this all looks correct in my eyes and very useful info CT owners should have.
but what is FOM?

 

[ajdelange]

Figure Of Merit. Engineerspeak.

 

[TyPope]

That's exactly what you have every time you see a U-haul. Some boat trailers have an arrangement whereby the hitch pushes back on a hydraulic piston thus applying braking automatically. I guess that works to some extent.

I never worry about professional drivers... It's when homeowner Dave decides to rent a Uhaul trailer and isn't used to towing that scares me. Even though most, if not all Uhaul trailers have surge brakes, it's not the same as having trailer brakes.

I didn't know Tesla didn't offer trailer brake control in the Model X. Hmm... All the truck producers do and Tesla would be remiss to not at least meet that requirement from the factory.

 

[ajdelange]

The one time I rented a U-haul (small) it had no brakes whatsoever. I swore I would never patronize them again.

My Lexus is essentially the same as the Tesla. It has a place to plug in something like a Prodigy but nothing internal. A Prodigy is a pretty simple gadget in concept. It has an inertial sensor that sends a DC signal to the trailer based on the amount of negative acceleration it senses and a scaling factor the driver sets up. The Tesla has the sensors, of course, but does not, AFAIK, generate the brake signal.

Note that the concept of the surge brake is the same as the Prodigy. Decelleration produces a hydraulic signal in the former and sensing mass is the trailer itself whereas with the Prodigy the sensor is a small mass within the unit and the signal is electric.

 

[ajdelange]

But I'd guess towing 5000lb will probable come with a 40-50% penalty over mountains.

People always want to know how much towing will reduce their range. It is an impossible question to answer as it depends on so many things. But there is one exception and that is to consider what would happen were you towing another CT (which Tesla isn't going to allow but that doesn't matter). The load being towed would, in that case, have the same drag (approximately as the tow vehicle might shield it some) and the same mass. Rolling resistance would be the same and you wouldn't achieve the benefits of regenerative braking but approximately speaking the energy required to move it a mile will be pretty close to the energy required to move the towing vehicle a mile. Thus the range will indeed come down to about 1/2. Mountains or not.

 

[ajdelange]

Note: Thanks to the eagle eye of @Newton an error in the program was discovered. All the numbers in this post have been edited to reflect correction (at least we hope we got it fixed) of that error. The end numbers do not change much and conclusions drawn from them do not change at all.

The reduction in range won't be the same mountains or not. There will be a bigger reduction in range the harder the motors need to work to get up an incline. While this is true for a vehicle not towing it won't be a linear response at all with double the weight scenario you gave.

Here are some loads for a 5000 lb vehicle on flat terrain. The first one represents a CT with no load. Note that regen is on.

5000 lbs Speed 50 to 20 Avg 41.9 mph, 0.0 ± 0.0 %grade , Wh/mi Total: 355.4, Drive: 33.4, Slip: 66.0, Drag: 167.9, Roll: 87.9. Gravity: 0.0, Inertial: 0.2; Regen. On, Brake 0.0

This one is for another 5000 lb vehicle with the same rolling resistance and weight. It represents a towed load. A towed load has no regen so it is off.

5000 lbs Speed 50 to 20 Avg 41.9 mph, 0.0 ± 0.0 %grade , Wh/mi Total: 507.5, Drive: 33.4, Slip: 66.0, Drag: 167.9, Roll: 87.9. Gravity: 0.0, Inertial: 0.2; Regen. Off, Brake 152.1

As a passively towed vehicle has no slip loss or drive train losses we need to take out 33.4 + 66 Wh/mi for a total of 408.1 Wh/mi for the towed vehicle. Thus range is reduced to 355.4/(355.4 + 408.1) = 46.5%


Now doing the same thing for a 4% grade:

5000 lbs Speed 50 to 20 Avg 41.9 mph, 4.0 ± 0.0 %grade , Wh/mi Total: 788.7, Drive: 48.6, Slip: 93.8, Drag: 167.9, Roll: 87.8. Gravity: 390.4, Inertial: 0.2; Regen. On, Brake 0.0

5000 lbs Speed 50 to 20 Avg 41.9 mph, 4.0 ± 0.0 %grade , Wh/mi Total: 877.6, Drive: 48.6, Slip: 93.8, Drag: 167.9, Roll: 87.8. Gravity: 390.4, Inertial: 0.2; Regen. Off, Brake 88.9

Again we take off the slip and drive train loads giving a load for the towed vehicle in this case of 735.2 Wh/mi and the range reduction attributable to it is then 788.7/(788.7 + 735.2) = 51.7%

So as I said, the reduction in range is about the same, mountains or not.

 

[ajdelange]

"They" can't improve on this but you can. Minimize towed weight which means if you can put it in the truck bed rather than in the trailer do that. If you put it in the truck bed you can recover much of its inertial load through the truck's regen system. If it's in the trailer that energy goes to warm the brakes. Keep the frontal area and drag coefficient of the trailer down to the extent possible. What this really means is that if you can't put it in the truck bed put it inside the trailer i.e. out of the airflow. Drive slowly at as uniform a speed as possible (autopilot helps with this). Accelerate slowly. Don't use the brakes unless necessary.

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