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Given that acceleration is inversely proportional to mass, assuming constant wind resistance for a given speed, would a heavier truck be more efficient at cruise than a lighter truck, all else equal?

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    Heavier would use more fuel going uphill, but less going down... Is cruise horizontal?
    – Tim
    Commented Jul 12, 2021 at 16:59
  • @tim what is the physics behind heavier using less fuel going down hill?
    – HandyHowie
    Commented Jul 12, 2021 at 17:12
  • @HandyHowie, I think what Tim was saying is that the heavier vehicle uses less gas going down a hill than they use going up, not less than another vehicle going down a hill. Commented Jul 12, 2021 at 17:24
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    @HandyHowie - ever tried even walking uphill/downhill?!
    – Tim
    Commented Jul 12, 2021 at 17:38
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    Gravity is a myth, the earth sucks... uphill against gravity...
    – Solar Mike
    Commented Jul 12, 2021 at 17:41

3 Answers 3

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As you said, if you ignore wind resistance, you have 2 remaining forces on a vehicle, gravity and friction.

On a level surface, you can ignore gravity to some extent because it is acting perpendicular to the direction of movement. Of course gravity will be having an effect on the vehicle causing friction between the tyres and the road. So discounting gravity, the only force remaining is friction. It is more than likely the case that a heavier vehicle will have greater frictional forces acting on it - between the tyres and the road and in the other moving parts. So at a constant velocity the lighter vehicle will be more efficient.

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In practical reality, "all else equal" means next to nothing.

With a heavier vehicle, you have a larger tire meaning you have a larger contact surface with the ground, meaning more friction with the road. You also have a larger engine, which usually means it also has more friction and is generally less efficient. Part of this is because the parts are larger and have a higher inertia to overcome.

A heavier vehicle also tends to have a larger body, causing more air resistance. You mention "constant wind resistance", yet you don't mention which direction it's coming from. It makes a difference if it's head on or a from the rear, since a tailwind can help a large vehicle more than a smaller vehicle, just as a headwind will hurt the mileage of a large vehicle more than a smaller car. Even a side wind will affect a large vehicle's fuel mileage differently than a smaller vehicle.

As mentioned in a comment by Tim, does this "cruise" include hills? That changes mileage on most vehicles significantly.

And does "cruise" mean letting off the gas completely? Even for short periods?

Anecdote

Before I get into real world examples, I'll talk about two trips I took about 2 years ago, which happen to be the same trip, excluding an accidental wrong turn.

I moved to Las Vegas from Iowa. It was almost exactly 2000 miles, going through Oklahoma to avoid snow and ice in the mountains during the time of year I moved. The moving truck was a Ford F650, with a 26 ft bed and towing one of my cars. I didn't have the back completely filled, but there was significant weight back there, with all the tools and other stuff I had in it.

Every 2 hours or so, I had to stop to fill the tank. I don't remember exactly how large it was, but I promised my dad to fill it when it got below half a tank. There were times when I put $70-100 of gas into the truck after those 2 hours. I also had to had to keep my foot pressed into the gas the whole time, when I wasn't going down a steep hill, anyway. I also had to up and downshift regularly when dealing with hills. There were hills I had to downshift just to use the engine as a brake so I didn't burn up the actual brakes.

Fast forward 3 months later when I flew home to get my other car. Gas prices hadn't changed much and I drove my other car the same route, except for that accidental 30 mile detour.

I was able to easily go 3-4 hours without having to refill a 14 gallon tank. Granted, I didn't obey the "half a tank" rule, but refilling that was $30-40 dollars for the 3-4 hours, rather than +$70 for 2 hours.

I also didn't have to downshift for hills. Downshifting means that you have a higher RPM and are using more gas for the same distance, since you are trading lower mileage for higher power to the wheels.

Efficiency

What does that mean to you? Does that mean more work done for less effort or more product hauled for less gas per pound/kilogram? Or does it mean something else? Does it mean fewer trips for a larger vehicle than a smaller one? I doubt the last one based on your Question, but it's something some people might be thinking about.

Real world numbers

On average, semi-trucks get only 6.5 miles per gallon. Their efficiency ranges wildly between 3 mpg going up hills to more than 23 mpg going downhill.

https://www.arrowtruck.com/blog/2016/06/21/manage-your-semi-trucks-fuel-use-with-these-tips/

This link lists mid-sized pickup trucks that are around 22 mpg. It also has full sized pickup trucks 21-25 mpg, and diesel trucks from 21-27 mpg.

https://www.edmunds.com/truck/articles/best-gas-mileage-trucks/

This site lists a variety of car styles with a range of 26-142 mpg, with typically the smallest cars getting the better mileage.

https://www.fueleconomy.gov/feg/best-worst.shtml

These are all tested "empty", except for the semi trucks. They are also all estimated, since the actual use of the vehicle determines what the actual mpg is at any given time.

And then there's trains, which take the cake when it comes to ground travel and fuel economy. There's a lot of differences between a train and a typical road vehicle, though.

The 2018 CSX system-wide train efficiency metric equals:

208,712,027,000 ton-miles / 423,998,863 gallons = 492 ton-miles per gallon.

In other words, CSX trains, on average, can move a ton of freight nearly 500 miles on a gallon of fuel, based on our 2018 revenue ton miles and 2018 fuel use.

https://www.csx.com/index.cfm/about-us/the-csx-advantage/fuel-efficiency/

Government statement on weight of vehicles

Let's start with the easy and simple numbers. The EPA says that for every 100 pounds taken out of the vehicle, the fuel economy is increased by 1-2 percent. Based on a gallon of gasoline costing $2.58, this translates to savings of between $0.03-$0.05 a gallon. Of course, 100 lbs. in a small hatchback is going to make a bigger difference than those same 100 lbs. in a Tahoe, so make reasonable assumptions about what going lightweight can offer you.

For a more detailed look at what's possible, consider a report issued by the Aluminum Association, Inc. based on research by Ricardo. The chart below shows that for a small car with a 1.6-liter engine, reducing weight by five percent led to an increase in fuel economy of 2.1 percent on the EPA combined rating. Eliminating ten percent of the weight provides a 4.1 percent mileage boost and a dramatically significant twenty percent weight decrease improved fuel economy by 8.4 percent.

https://www.autoblog.com/2009/10/29/greenlings-how-does-weight-affect-a-vehicles-efficiency/

So the EPA says that not only will weight reduction help your vehicle's fuel economy, it will depend greatly on your vehicle's engine: A smaller engine will have a greater difference for weight added or reduced than a larger engine.

The article even says that automakers are getting in on reducing vehicle weight to increase fuel economy. This is earlier in the same article as above.

Over the last few decades, the average weight of a vehicle sold in the U.S. climbed steadily after surviving the oil embargoes of the 1970s. Today, however, auto companies are putting a lot of effort into reducing weight – Lotus set up an entire lightweight structures division, BMW is investing millions in the production of carbon fiber and Jaguar loves aluminum – because every ounce you take out of a car improves the vehicle's performance and fuel economy. Options for weight savings that automakers are investigating include installing things like plastic fuel tanks and using carbon fiber instead of steel. As we discovered in a previous Greenlings, carbon fiber is a remarkable, lightweight substance that will begin see wider use as prices (invariably) come down.

Inertia

Oh, there are quite a few things to be said about this. Some are true and many are misunderstandings.

First off, a semi truck running a red light because they can't stop in time is partly due to inertia, but there's a lot of other factors involved, even when ignoring driver error.

Semi trucks could have the ability to stop in the same amount of time as a car, but it would significantly larger brake pads. It would also need significantly wider tires to make the bigger brakes effective, since even with the current brake system, semi's will lock up their tires and still not be able to stop. There's lots of physics that go into that, including the fact that a rolling tire has more friction with the road than a sliding tire, but that's not what you're looking for in an Answer. It's also plenty complicated.

But that inertia, that idea of the semi going through a red light, is where your idea is based, whether you know it or not. Maybe not, since I'm just guessing here, but it seems like a "normal" conclusion.

Getting into physics a bit, the equations for force are a great place to start:

F = ma; Force equals mass multiplied by acceleration
or another way to state it, meaning the same thing is:
F = (1/2)mv2; Force equals one half of mass times velocity squared

The Force (F) is the amount of force it'll take to move an object. Just looking at those 2 formulae, you should notice that mass is a significant factor in them. If you double the weight of something, it'll take double the Force to move it. The caveat here is that it's assuming a frictionless plane.

In the example of trucks, there's considerable amount of friction. The rolling friction of the wheels, the internal friction of the engine and transmission, the air friction, and many others that are getting off topic. As I mentioned earlier, a larger truck has a lot more friction to worry about than a smaller truck, but what if we simply used the same truck with different weight in it? Well, the rolling friction is still altered because the tires will deform and the suspension will have changed it's height, causing air resistance/friction to be different, including the ground effect under the vehicle.

There's just so many reasons/variables why it's extremely difficult to determine how weight affects gas mileage that without actual test cases, you're not going to get any answers. Along with that, different vehicles will have different results, as will different drivers, and different weather on different days.

Conclusion

There are probably college courses specifically on fuel efficiency, due to how complicated the equations of inertia, friction, and the other variables are and how they interact with each other. I went through physics in college many years ago, and I sure don't know how it all fits together well enough to give you anything close to a definitive answer.

But as the EPA states (mentioned earlier), a lower weight means better fuel economy, but there are a lot more factors to fuel efficiency than just weight. And there's plenty that can be said about EPA mileage estimates, but I was just using that as baseline numbers for comparison, not as absolute empirical proof.

Because of all the reasons I stated previously, you aren't likely going to get a good answer for your question. You'd likely get an answer on Physics, but that's likely only going to be of limited value, too, since it likely won't deal with more than just a few specific cases.

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    1/2mv^2 is a unit of energy, not force. I don't really understand the point of the anecdote section, in which you drive two vehicles with different fuel economies, gas tank sizes, weights, and aerodynamics. There's too many moving parts there to be able to assess the contribution of weight alone - all it shows is that an F650 is less fuel efficient than a car, but sheds no light at all on the reason why. You say having two cars of different weight with "all else being equal" is difficult to achieve, but it's actually very easy - just use one car and throw some sandbags in the back. Commented Jul 12, 2021 at 19:08
  • @NuclearHoagie, I put in that story to show just how difficult it is to calculate fuel economies based on weight alone. Also, "throwing sandbags in a trunk" is exactly what I was talking about when I mentioned how the suspension would cause a difference in air resistance and the tires deforming causing differences in the test that will affect the results, not just the added weight. Commented Jul 12, 2021 at 19:11
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"All else being equal", a heavier vehicle will use more fuel at level cruise when compared to a light one. There is more friction between the tire and road surface, effectively increasing the rolling resistance. You would be able to see this visually as deflection in the sidewalls of the tire on each revolution. Heavier vehicle means more deflection, more resistance.

You would also get an incremental increase in friction at other components that support the weight, such as wheel bearings, but the tires would cause the majority of the increase.

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