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Lightweight trailers a Model 3 might be able to tow

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I hope this super simplified example helps further explain the effects I described. The Model 3 will have lots of power and it's size and weight will make towing small trailers safe. However, it's rather extreme efficiency, as compared to even a small travel trailer, is atypical and many owners will likely be surprised by these effects.
Was reviewing this thread and realized that I had forgotten to thank you for your last post that did such a nice job of explaining the position you had posted about upthread.

I've also been reviewing the towing threads in the Model X forum and am becoming somewhat pessimistic about the possible Model 3 towing range. While I expect the 3 to have a battery option that provides a range comparable to the largest battery available on the S in late 2017, @Zoomit has made clear that the maximum 3 range when not towing is likely to be reduced by at least 50% when towing even a smallish camper trailer, and it could be reduced by much more than 50%. In which case it wouldn't be a useful tow vehicle for me, though it still might work for some people.

Since I started this thread I have had the opportunity to see an Alto trailer in person and I really liked it. I refuse to buy an ICE ever again, so now have to figure out how to tow it with a Tesla...
 
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So in the following example, the size of the wake equals the drag of the vehicle. The trailer by itself needs 10 units to move. The big car needs 4 and the "small aero efficient" car needs 2 units. When pulling, the wake of the vehicles is combined and so the trailer wake dominates the numbers and the wake size & drag force is 10 units. (This is definitely over simplified but representative.)
I appreciate that explanation and the caveat that it is "over simplified". Now I would like to apply it to real world examples. Here are frontal area calculations for two trailers I am considering:

Alto R-1723 trailer (retractable roof): 83"(h) x 83"(w) = 6,889 sq in / 144 = 47.84 sq ft frontal area, 1,725 lbs dry weight

Alto R-1743 trailer (fixed roof): 95.5"(h) x 86"(w) = 8,213 sq in / 144 = 57 sq ft frontal area (19% greater), 1,592 lbs dry weight

Given that both trailers have similar shapes, does a 19% greater frontal area equate to 19% greater energy usage by the same tow vehicle? Or is the greater energy usage (because obviously there will be some increase in energy usage) in some way a function of the towing speed? I acknowledge that the difference in weight between the two trailers has essentially no impact on towing energy usage, which is primarily determined by aerodynamic drag and secondarily by rolling resistance. I have found many references online where ICE owners compare MPG while towing two different trailers, one about twice the weight of the other, and find just a 4-8% difference in energy usage if the shape of the two trailers is roughly the same.

Now for comparing the frontal area of these two potential tow vehicles:

Model 3 56"(h) x 74"(w) = 4,144 sq in / 144 = 28.8 sq ft frontal area

Model X 66"(h) x 81.5"(w) = 5,379 sq in / 37.4 sq ft frontal area (32% greater)

Obviously the X has a significantly greater frontal area. Just as obviously we know that the 3 will be significantly more energy efficient, but we don't yet know how much more. Still, it seems reasonable to assume at least 25% less energy usage over a given distance for the 3 compared to the X (when not towing).

I am wondering if there is a way to quantify and then correlate tow vehicle frontal area, tow vehicle energy efficiency, and trailer frontal area and come up with a set of curves showing how they relate to each other. This is beyond my mathematical abilities, but hopefully not beyond my comprehension if described and plotted.
 
The equation of energy consumption of a wheeled vehicle is:

Energy = 1 / Drive train efficiency * [(1/2 * Mass * Regen efficiency * Velocity^2 / distance between stops) + (1/2 * density of air * Frontal area * Drag coefficient * Velocity^2)]

From this one can see that: Mass only matters if you stop a lot. Frontal area and drag coefficient both matter at high speeds. Higher speeds rapidly get outrageous in energy consumption.

Caveats: Frontal area should probably be the larger of the car or the trailer. Drag coefficient is complicated for a towed vehicle, but taking the larger (plus a bit) *might* work. More efficient vehicles tow more efficiently, but the greater percentage of their energy goes to the towed vehicle, making range drop drastically.

Thank you kindly.
 
I appreciate that explanation and the caveat that it is "over simplified". Now I would like to apply it to real world examples. Here are frontal area calculations for two trailers I am considering:

Alto R-1723 trailer (retractable roof): 83"(h) x 83"(w) = 6,889 sq in / 144 = 47.84 sq ft frontal area, 1,725 lbs dry weight

Alto R-1743 trailer (fixed roof): 95.5"(h) x 86"(w) = 8,213 sq in / 144 = 57 sq ft frontal area (19% greater), 1,592 lbs dry weight

Given that both trailers have similar shapes, does a 19% greater frontal area equate to 19% greater energy usage by the same tow vehicle? Or is the greater energy usage (because obviously there will be some increase in energy usage) in some way a function of the towing speed? I acknowledge that the difference in weight between the two trailers has essentially no impact on towing energy usage, which is primarily determined by aerodynamic drag and secondarily by rolling resistance. I have found many references online where ICE owners compare MPG while towing two different trailers, one about twice the weight of the other, and find just a 4-8% difference in energy usage if the shape of the two trailers is roughly the same.

Now for comparing the frontal area of these two potential tow vehicles:

Model 3 56"(h) x 74"(w) = 4,144 sq in / 144 = 28.8 sq ft frontal area

Model X 66"(h) x 81.5"(w) = 5,379 sq in / 37.4 sq ft frontal area (32% greater)

Obviously the X has a significantly greater frontal area. Just as obviously we know that the 3 will be significantly more energy efficient, but we don't yet know how much more. Still, it seems reasonable to assume at least 25% less energy usage over a given distance for the 3 compared to the X (when not towing).

I am wondering if there is a way to quantify and then correlate tow vehicle frontal area, tow vehicle energy efficiency, and trailer frontal area and come up with a set of curves showing how they relate to each other. This is beyond my mathematical abilities, but hopefully not beyond my comprehension if described and plotted.
Before addressing your final question, let me comment on a few things:

-- The differences between these two trailers is significant. They do not have similar shapes. The fixed roof trailer will have more friction drag and pressure drag. It has a larger wetted area and thus the skin friction drag will be higher. It also has a more blunt rear shape resulting in higher pressure drag. In addition, it is a foot taller, all of which is clearly above the wake of the tow vehicle. So it's pretty easy to generalize that the fixed roof trailer will require more than 19% greater energy to tow than the retractable roof variant. I wouldn't be surprised if it was 50% or even a 100% greater. Using a simple comparison of only frontal area, the retractable trailer frontal area is 28% larger than the Model X frontal area [47.8/37.4]. The fixed roof trailer is 52% larger than the Model X [57/34.7]. That's an 85% increase right there [52/28], using a comparison method that DOES NOT account for the poorer Cd of the fixed roof trailer.

-- Faster speeds will alway require more energy, at least at speeds where a significant portion of the energy required is due to overcoming aerodynamic drag losses (>25 mph).

-- You are correct. The differences in weight between these trailers does not have a significant effect on the towing efficiency and range.

There is no easy way to quantify the effects and create a set of curves. This is because the results are heavily dependent on the aerodynamic interaction of the two vehicles. Even if you could assume each vehicle maintained the same Cd as you grew or shrunk it in size, the relative sizes, and specifically the location and size of the tow vehicle wake, makes the results very nonlinear. I could make simplifying assumptions and try to capture how they interact intuitively, but it wouldn't be appropriate to extrapolate that out to the four different vehicles you're considering.

And maybe this is where I'll offer a more direct opinion. The difference in range between the fixed and retractable roof models will be significant. Based on the TeslaXCanada experience, I'd consider a 90 or 100kWh battery to be the minimum to pull the retractable roof trailer. The fixed roof trailer would be too much of a compromise in range and flexibility based on my expectations for even infrequent long distance travel. Similarly, the Model 3 may be reasonable to pull the retractable roof trailer, if or when it has a ~90kWh battery. Any vehicle with less than 90kWh would likely be too much of a compromise in range and flexibility for me.

Remember, for the tow vehicles and trailers we're talking about, the single greatest use of energy to move the combined vehicles on the highway is the energy needed to overcome trailer drag. For a trailer this size, increasing the tow vehicle battery capacity is the most effective way to provide longer range. A theoretical Model 3 100D would tow this trailer further than an X 90D.
 
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From this one can see that: Mass only matters if you stop a lot. Frontal area and drag coefficient both matter at high speeds. Higher speeds rapidly get outrageous in energy consumption.
I generally agree, but mass matters tremendously with elevation change as well. There's an argument that you get (some of) it back on the descent, but when you're looking to make it from one charging station to another, weight can be an important factor in the mountains.
 
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I generally agree, but mass matters tremendously with elevation change as well. There's an argument that you get (some of) it back on the descent, but when you're looking to make it from one charging station to another, weight can be an important factor in the mountains.

I was being loose with my 'stop a lot'; braking even if you don't come to a complete stop, counts. You get all of it back on descent (potential to kinetic energy conversion is 100% efficient). You lose some of that if you need to brake (regen or otherwise) to maintain a safe speed. But that falls under the braking losses, so just consider it another stop in the equation.

Thank you kindly.
 
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I was being loose with my 'stop a lot'; braking even if you don't come to a complete stop, counts. You get all of it back on descent (potential to kinetic energy conversion is 100% efficient). You lose some of that if you need to brake (regen or otherwise) to maintain a safe speed. But that falls under the braking losses, so just consider it another stop in the equation.
Agreed, but to be clear what I mean is that in most cases the elevation gain isn't net zero between charging locations. In the cases that are concerning, it's a large gain between stops, and mass is an absolutely crucial consideration.

As an example, @jackbowers has concerns about making it over Donner Pass with his lightweight, very aerodynamic Bowlus Road Chief. This is a trailer that, when towed flat at 55mph, represents only about 120% of the standard Model X consumption.
 
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The difference in range between the fixed and retractable roof models will be significant. Based on the TeslaXCanada experience, I'd consider a 90 or 100kWh battery to be the minimum to pull the retractable roof trailer. The fixed roof trailer would be too much of a compromise in range and flexibility based on my expectations for even infrequent long distance travel. Similarly, the Model 3 may be reasonable to pull the retractable roof trailer, if or when it has a ~90kWh battery. Any vehicle with less than 90kWh would likely be too much of a compromise in range and flexibility for me.
Thank you very much for your analysis! It appears that my willingness to consider the Alto F1743 fixed roof trailer was an exercise in wishful thinking. I am going to order the Alto R-1723 trailer, the same one that @fortytwo has. All I need to do for now is put down a deposit which is fully refundable up to 4 months before delivery, and delivery will not be until the beginning of 2018. Long before then we will know what the Model 3 battery size options will be (refresher for those reading this post: I will be trading my S in on a 3). If the biggest Model 3 battery is less than 90kWh then a Model 3 is very likely not going to work to tow a trailer the size of an Alto (it may work for much smaller trailers but I'm not willing to go smaller). In which case I will have to reconsider my Model 3 order. Obviously the X would be my only choice for towing a trailer like an Alto if the largest Model 3 battery is less than 90kWh.

I am optimistic that the largest Model 3 will be very close to or equal to 90kWh. Even though the 3 chassis is smaller than the S chassis, the 3 will be using the new generation cells produced at the Gigafactory, cells with more energy than those currently used in the S/X.

I do not believe that Tesla will decide to restrict the 3 to a battery size that results in less range than the S with its largest battery option. Currently the S P100D is rated at 315 miles. When the S 100D is available next year (that seems certain to happen in my opinion) the range will be slightly higher, likely around 330 (5% more than the P version). Since the 3 is more efficient it seems reasonable to believe that a Model 3 90D will achieve at least the same range and possibly slightly more (Note: I think it unlikely that when the 3 goes into production Tesla will be able to offer it with a 100kWh battery).

That said, as @Zoomit made clear upthread, the higher efficiency 3 will take a bigger range hit when towing than a lower efficiency car like an S or an X. So if we postulate a Model 3 90D having an EPA range of at least 330 and then assume that when towing at 55mph range will drop by 55% that is 149 miles. I could live with that. But if range drops by 60% at 55mph that may be too much for me. Then I will have to seriously consider a Model X. I don't want a car that big, I have no use for the Falcon Wing doors (no kids or pets, would rarely use the second row) and do not want to pay the heavy price premium of the X over the 3, but if I want to tow that could be the only option available.
 
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Bjorn Nyland has posted this video summary of the energy consumption pulling a variety of trailers with his X P90D.


He extrapolates down to the 60D, which might be close to the Model 3 and relevant for this thread.

Be aware, he's assuming 50 mph for this data. I don't feel that's fast enough to be safe on US highways, so I'd certainly plan for faster speeds and hence expect shorter range. Also, increasing speed from 50 to 57 mph increases energy consumption (decreases range) by about 30%! [57^2/50^2]
 
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Also, increasing speed from 50 to 57 mph increases energy consumption (decreases range) by about 30%! [57^2/50^2]
That's assuming that aerodynamic drag is the exclusive factor at those speeds. It gets more complicated if rolling resistance and other efficiency measures account for, say, 40% of drag forces. Then you can only assign an 18% difference to that speed increase (0.6 * 0.3).
 
That's assuming that aerodynamic drag is the exclusive factor at those speeds. It gets more complicated if rolling resistance and other efficiency measures account for, say, 40% of drag forces. Then you can only assign an 18% difference to that speed increase (0.6 * 0.3).
Yes, this is an important caveat.

Let's play with math and see how close my 30% approximation was. My very speculative energy consumption model for the Model 3 shows that aero drag and subsequent drivetrain losses account for 80 Wh/mi (or 43%) of the 188 Wh/mi used for steady 50 mph travel. At 57 mph, that term driven by aero drag is now 105 Wh/mi (50%) of the total 210 Wh/mi used. Energy usage increases only 12% [210/188] to go faster, not 30%.

Pulling something like a 6'x8' enclosed trailer, let's assume the aero drag and subsequent drivetrain losses now account for 530 Wh/mi (83%) of the 637 Wh/mi used at a steady 50 mph. At 57 mph, that term increases to 689 Wh/mi (87%) of the total 794 Wh/mi used. That represents a 25% increase [794/637] due to the extra 7 mph, not 30%.

Because I have the model tweaked for this calculation, and my caffeine is kicking in, let's increase the speed another 7 mph with the trailer and see what happens...the aero drag term increases to 868 Wh/mi (89%) of the 972 Wh/mi total at a steady 64 mph. That represents a 22% increase [972/794] due to the extra 7 mph. That compares similarly to a rough approximation of 26% [64^2/57^2].

Now for more giggles, here are the available ranges for the above scenarios, assuming the Model 3 has a 53 kWh usable battery capacity.

Model 3 only
50 mph: 282 mi
57 mph: 253 mi
64 mph: 225 mi

Model 3 with enclosed trailer
50 mph: 83 mi
57 mph: 67 mi
64 mph: 55 mi

There are a bunch of hand-wavy assumptions in all the above calculations, so please don't assume the numbers are correct. They're probably close, but the trends are what's important to understand.
 
Pulling something like a 6'x8' enclosed trailer, let's assume the aero drag and subsequent drivetrain losses now account for 530 Wh/mi (83%) of the 637 Wh/mi used at a steady 50 mph. At 57 mph, that term increases to 689 Wh/mi (87%) of the total 794 Wh/mi used. That represents a 25% increase [794/637] due to the extra 7 mph, not 30%.
Keeping in mind your caveat about the speculative nature of these calculations, I'm going to go ahead and dissect this a little with you. Mostly I'm curious about your model. In this paragraph, you're attributing 107 Wh/mi to rolling resistance (et al) at 50 mph and 105 Wh/mi at 57 mph. I'm assuming these are estimations, and you're keeping rolling resistance constant? If so, you're assuming a flat plane of a roadway, correct?

I often see it repeated is that rolling resistance and aero drag are about equivalent in the 50 mph speed range for the vehicle only. At what velocity is there equivalence in your model for just the Model 3? How about for the Model 3 and trailer?

Thanks, I find all of this pretty fascinating.
 
Keeping in mind your caveat about the speculative nature of these calculations, I'm going to go ahead and dissect this a little with you. Mostly I'm curious about your model. In this paragraph, you're attributing 107 Wh/mi to rolling resistance (et al) at 50 mph and 105 Wh/mi at 57 mph. I'm assuming these are estimations, and you're keeping rolling resistance constant? If so, you're assuming a flat plane of a roadway, correct?

I often see it repeated is that rolling resistance and aero drag are about equivalent in the 50 mph speed range for the vehicle only. At what velocity is there equivalence in your model for just the Model 3? How about for the Model 3 and trailer?
Energy consumption per unit distance due to tire rolling losses is constant in the model and I'm assuming no elevation changes. In this thread, Model 3 Battery size, I posted a graph that showed the speed in my model where aero drag and rolling resistance are equal. Looks like it's around 54 mph, where the blue and orange lines cross in the upper left graph.

In my previous post in this thread, I did not calculate any changes to rolling resistance consumption due to the trailer. (This was a simplifying shortcut since rolling resistance consumption is flat vs speed.) But if I assume the cargo trailer is 2500 lbs with tires that have the same rolling resistance coefficient as the Model 3 tires (a WAG at 0.0088), then the speed where aero drag and rolling resistance are equal is ~26 mph.
 
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@Zoomit thanks so much for your continued participation in our EV towing discussion/obsession I find it fascinating. I hope that by the end of 2017 we will have real kWh/mi towing energy usage for the Model 3 as well as more extensive Model X towing data. With so few Tesla owners towing at this point, and only a fraction of those owners participating on TMC, our available data set is pretty thin.
 
I'm looking at the Little Guy T@b at 15 ft and 1600#. It even has a wet bath.
IMG_1051.jpg
 
Nice little trailer. How much does it cost with the wet bath? Compare it to this Alto Safari Condo which is 17 ft overall, 1600 lbs dry, has a wet bath, inside kitchen, queen size bed and separate 2 person seating area, base price less than US$30K. But there is a 16 month wait after you place your order.
I'm looking at the Little Guy T@b at 15 ft and 1600#. It even has a wet bath.View attachment 223605