RPM vs Gas Consumption

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RPM vs Gas Consumption

Postby askeeve » Tue Jan 17, 2012 7:09 pm UTC

Got into a little debate with some coworkers during lunch today and though I've never posted here before I thought you folks might be interested.

A coworker stated that two (equal) cars running at equal RPMs but different speeds (and thus different gears) over equal terrain will consume the same gas.

From our discussion it seems like we were all missing something about how cars work in our arguments though a few of us (not me) are fairly serious gearheads. I would appreciate any input on this.

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Re: RPM vs Gas Consumption

Postby Obby » Wed Jan 18, 2012 4:22 pm UTC

While I'm not a gearhead, my understanding is the following:

Given your situation (same RPM, same engines, different gears), both engines would consume gas at the same rate. That is, if these two engines were to run at this RPM and speed until they ran out of gas, they both would run out of gas at the same time.

However, the car that was in the higher gear would have traveled further over that time. Thus, while rate of consumption would be the same, the efficiency of that consumption would be much different between the cars. The slower car would be at a lower miles-per-gallon rate than the faster car would be.

I may be wrong, but that has been my understanding of these things.
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Re: RPM vs Gas Consumption

Postby askeeve » Wed Jan 18, 2012 4:46 pm UTC

A counter-argument to this (again, I'm not taking a side personally) is that at a higher velocity, more energy is required to move the car and thus without actually increasing the RPMs, more gas is needed to generate that higher force. Running through conservation of energy theories we decided that a side effect of this would likely be increasing pressure in the engine somehow.

Is the premise of this theory valid?

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Re: RPM vs Gas Consumption

Postby gmalivuk » Wed Jan 18, 2012 4:47 pm UTC

Yeah, maintaining the same RPM on a higher gear with more resistance is going to take more energy, and hence more gas.
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Re: RPM vs Gas Consumption

Postby askeeve » Wed Jan 18, 2012 7:02 pm UTC

It is true however that traveling at a greater speed with the same fuel consumption as a lower speed is equivalent to better gas mileage.

I would assume that though you're spending a little more gas at the higher speed to maintain the same RPMs, your net mileage is still better correct?

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Re: RPM vs Gas Consumption

Postby gmalivuk » Wed Jan 18, 2012 7:43 pm UTC

Most cars have their maximum gas mileage at surprisingly low speeds around 50-60mph, actually. Faster than that and you're fighting too much air resistance to get good efficiency.
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Re: RPM vs Gas Consumption

Postby JBJ » Wed Jan 18, 2012 7:59 pm UTC

askeeve wrote:It is true however that traveling at a greater speed with the same fuel consumption as a lower speed is equivalent to better gas mileage.

I would assume that though you're spending a little more gas at the higher speed to maintain the same RPMs, your net mileage is still better correct?

I'm afraid not. Cars have to overcome both rolling resistance and air resistance. Rolling resistance doesn't change much with speed. Air resistance does. The faster you go, the more work has to be used to overcome drag, and more fuel is used.

The thing is, RPM does not equivalent to fuel used. This is apparent if you've ever driven up a steep slope or pulled a heavy load in a vehicle. Say you're driving along on a flat road at 45 mph, and the engine is going at, say, 2000 rpm. You come to a steep hill. As you go up, you notice that to maintain your 45mph speed in the same gear, you have to give it more gas. The engine is turning at the same RPM, you're going the same speed, but because of the extra load (going uphill) you are now using more fuel just to maintain the same speed.
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Re: RPM vs Gas Consumption

Postby moiraemachy » Wed Jan 18, 2012 11:54 pm UTC

JBJ wrote:The thing is, RPM does not equivalent to fuel used. This is apparent if you've ever driven up a steep slope or pulled a heavy load in a vehicle. Say you're driving along on a flat road at 45 mph, and the engine is going at, say, 2000 rpm. You come to a steep hill. As you go up, you notice that to maintain your 45mph speed in the same gear, you have to give it more gas. The engine is turning at the same RPM, you're going the same speed, but because of the extra load (going uphill) you are now using more fuel just to maintain the same speed.


Uh, this is something that always bothered me. I always thought that the gas pedal controlled the amount of fuel that feeds the engine every time it spins (regardless of the speed it's spinning), so fuel consumption would be directly proportional to the engine's rotation, and it would increase when the pedal is pressed. However, this model does not fit the claim that cars get their best mileage at 50~60mph (best mileage would be last gear, pedal not pressed)... does anyone know how the engine's rotation and the fuel consumption are really related? Does it even depend on how the engine is rotating?

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Re: RPM vs Gas Consumption

Postby Sagekilla » Thu Jan 19, 2012 12:58 am UTC

JBJ wrote:The thing is, RPM does not equivalent to fuel used. This is apparent if you've ever driven up a steep slope or pulled a heavy load in a vehicle. Say you're driving along on a flat road at 45 mph, and the engine is going at, say, 2000 rpm. You come to a steep hill. As you go up, you notice that to maintain your 45mph speed in the same gear, you have to give it more gas. The engine is turning at the same RPM, you're going the same speed, but because of the extra load (going uphill) you are now using more fuel just to maintain the same speed.


This is true if you're maintaining constant speed. Maintaining throttle doesn't cause you to use more fuel.
Also, fuel consumption is directly related to RPM and throttle.

moiraemachy wrote:Uh, this is something that always bothered me. I always thought that the gas pedal controlled the amount of fuel that feeds the engine every time it spins (regardless of the speed it's spinning), so fuel consumption would be directly proportional to the engine's rotation, and it would increase when the pedal is pressed. However, this model does not fit the claim that cars get their best mileage at 50~60mph (best mileage would be last gear, pedal not pressed)... does anyone know how the engine's rotation and the fuel consumption are really related? Does it even depend on how the engine is rotating?


Total fuel consumption is a product of the throttle and rotational rate of the engine. However, let's say you're maintaining a
constant speed, by keeping throttle at the same position. The moment you start climbing the hill, you experience a larger force
opposing your uphill movement. Your car is currently outputting the same power as it did when you approached the hill. The
same amount of power is being delivered to wheels, but a larger force is now opposing the direction in which you want to travel.

Therefore, you're seeing overall less power being delivered to your wheels even though you never changed your throttle.
Less power means your car is going to decelerate until it reaches a speed that it can maintain. Most people at this point
accelerate to maintain their original speed, which means that they're applying more throttle. If you make the assumption
that you're staying in the same gear, this means higher fuel consumption per second.

So applying throttle to maintain your speed going uphill is costing you more fuel. The proper thing to do is what's known as
"driving with load," which is just a fancy way of saying "Keep your throttle the same as it was when you first approached the
hill."

By maintaining throttle, you're not consuming more fuel than before. There is a real loss in fuel efficiency, but it's not because
of the way you're driving. Rather, it's due to gravity working against you as you try to climb uphill. If you stop accelerating slightly
before reaching the top of a hill, and let gravity accelerate you downward, you can regain some of the energy you lost in the uphill
climb as downhill speed.


Some other notes:
Spoiler:
When driving uphill, you may actually *gain* some small amount of fuel efficiency depending on your speed.
The reason is due to air resistance. The opposing force of gravity will rob you of speed. Air resistance is typically quadratic, so
if you go from a speed of v to v - dv, then air resistance will be 2 * dv * v - dv^2 times smaller than before.


tl;dr:
Fuel Consumption = Throttle * RPM
Keep throttle constant when going uphill, don't keep speed constant.
When going downhill, you should not be accelerating.
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Re: RPM vs Gas Consumption

Postby Qaanol » Thu Jan 19, 2012 3:06 am UTC

Somewhat off topic, but I feel rather strongly that all automobiles should be required to have a dash display that shows actual current fuel economy, both instantaneous and over the whole of the current trip. That way the driver can tell at a glance how many miles per gallon, or litres per kilometre, or amp-hours per mile, they are using right now.
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Re: RPM vs Gas Consumption

Postby Charlie! » Thu Jan 19, 2012 12:06 pm UTC

Sagekilla wrote:Keep throttle constant when going uphill, don't keep speed constant.

Public safety announcement: don't do this part on snow or ice. Potentially using less gas is not worth having trouble getting up the hill - drop into a lower gear and keep your speed consistent.

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Re: RPM vs Gas Consumption

Postby Hawknc » Thu Jan 19, 2012 1:04 pm UTC

Qaanol wrote:Somewhat off topic, but I feel rather strongly that all automobiles should be required to have a dash display that shows actual current fuel economy, both instantaneous and over the whole of the current trip. That way the driver can tell at a glance how many miles per gallon, or litres per kilometre, or amp-hours per mile, they are using right now.

Most cars I've seen have that, though the average is "since the driver last hit the reset button" in a lot of cases. If you're very interested, you can get devices that connect your car to your phone and record all sorts of interesting data, fuel consumption included, for graphing and analysis and general nerdery purposes.

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Re: RPM vs Gas Consumption

Postby Zamfir » Thu Jan 19, 2012 1:25 pm UTC

moiraemachy wrote:Uh, this is something that always bothered me. I always thought that the gas pedal controlled the amount of fuel that feeds the engine every time it spins (regardless of the speed it's spinning), so fuel consumption would be directly proportional to the engine's rotation, and it would increase when the pedal is pressed. However, this model does not fit the claim that cars get their best mileage at 50~60mph (best mileage would be last gear, pedal not pressed)... does anyone know how the engine's rotation and the fuel consumption are really related? Does it even depend on how the engine is rotating?

You are here confusing two things: on the one hand, the fuel consumption of the engine, and on the other hand the fuel consumption that you would need to make the engine deliver enough power to maintain your speed.

Of course, if you do not press the pedal, the engine will consume the least amount of fuel. Namely zero. At that point, the frictions in and around your car are simply sapping kinetic energy away from the car, so you lose speed.

The more relevant question is, at which speed do you need the minimum amount of fuel per kilometer to maintain that speed.

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Re: RPM vs Gas Consumption

Postby gmalivuk » Thu Jan 19, 2012 2:26 pm UTC

moiraemachy wrote:Uh, this is something that always bothered me. I always thought that the gas pedal controlled the amount of fuel that feeds the engine every time it spins (regardless of the speed it's spinning), so fuel consumption would be directly proportional to the engine's rotation, and it would increase when the pedal is pressed.
When there's more resistance to the rotation, you need more energy to maintain the same RPM. Which means more gas.
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Re: RPM vs Gas Consumption

Postby TrlstanC » Thu Jan 19, 2012 4:37 pm UTC

gmalivuk wrote:
moiraemachy wrote:Uh, this is something that always bothered me. I always thought that the gas pedal controlled the amount of fuel that feeds the engine every time it spins (regardless of the speed it's spinning), so fuel consumption would be directly proportional to the engine's rotation, and it would increase when the pedal is pressed.
When there's more resistance to the rotation, you need more energy to maintain the same RPM. Which means more gas.

And the gas pedal is actually the throttle pedal, it doesn't directly change the amount of fuel that's squirted in to the pistons (at least in the old fashion mechanical connections) it controls the throttle which keeps too much air from being sucked in to the cylinders. When your foot is off the pedal, the throttle just allows a tiny amount of air to be sucked in, just enough to keep the engine from stalling. The more you push the pedal down, the more the throttle opens up, and the more air the engine can suck in. Then there's some sort of electrical or mechanical control to squirt in fuel in proportion to the amount of air that's entering the engine on each revolution. If there was no throttle (or it was held wide open) the engine would just keep spinning faster and faster until something broke.

As the throttle opens up from a crack to slightly open to wide open the engine efficiency actually increases because it doesn't have to work as hard to pull air in to the cylinders. But as the car speeds up air resistance increases and it becomes harder to push the pistons down. There's a direct physical connection between the top of the pistons and the tires, there's a big mechanical advantage involved, both from gears in the transmission, and from the gearing of the wheels/tires. For every inch the piston travels down, the car moves forward quite a bit, but that also means that whatever effort is required to move the car forward is multiplied and is felt as resistance to pushing the piston down.

These two forces on the piston (actually spread across all the pistons in the engine, each at different parts of the combustion cycle) change (initially) in opposite directions as the engine's (and therefore car's) speed increases. As the throttle opens up there's less resistance from vacuum when the piston moves down, but there's more force resisting the piston's movement from the drive train. Initially efficiency increases, but as friction (both mechanical, and wind resistance) increases it will drop off, and this curve of increasing and then decreasing efficiency (fuel per revolution) will be slightly different for each gear, mostly due to the large increases in wind resistance at higher speeds. There may be spots where these curves intersect, where "same RPM = same fuel consumption" holds true, but that's an exception instead of the rule.

If instead of fuel and air combusting to power the engine, someone had to sit in the engine bay and push the pistons down by hand they would feel that it was more difficult to push them down if the car's traveling at 100mph at 5000rpm (in 5th or 6th gear) than if it was traveling at 30mph at 5000rpm in 2nd gear. In reality this translates in to the throttle being more open at higher speeds, and more fuel getting squirted in to cylinders in the same amount of time.

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Re: RPM vs Gas Consumption

Postby moiraemachy » Thu Jan 19, 2012 4:53 pm UTC

Sagekilla wrote:Fuel Consumption = Throttle * RPM


That's precisely what puzzles me: suppose the car is at the last gear, driving in a straight road. Since the engine is coupled to the wheels at a fixed ratio (the fifth gear's ratio), RPM is proportional to the speed you are going. Under these assumptions, the fuel used per distance traveled would be proportional to the throttle, and so pressing the gas pedal the least would result in a better mileage. Am I missing something?

Zamfir (emphasis mine) wrote:Of course, if you do not press the pedal, the engine will consume the least amount of fuel. Namely zero.


Is this the case? I'm pretty sure most modern engines can keep on running indefinitely when the gas pedal is not pressed, which would not happen if there was no fuel intake. I assumed that the throttle valve would always let some air in.

Also, sorry for kind of hijacking the thread OP. :oops:

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Re: RPM vs Gas Consumption

Postby Izawwlgood » Thu Jan 19, 2012 5:05 pm UTC

Could someone clarify something here:
RPM is a measure of how hard the engine is working. Nothing more, nothing less. So 'efficiency of travel' is a separate metric entirely. So, if you have one car driving uphill on tiny wheels, maintaining at, say, 4000 RPM, and the same car driving downhill on larger wheels, maintaining 4000 RPM, the second car will travel further on the same amount of gas.

The gas pedal is only influencing RPM. Right?
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Re: RPM vs Gas Consumption

Postby Sagekilla » Thu Jan 19, 2012 5:11 pm UTC

moiraemachy wrote:That's precisely what puzzles me: suppose the car is at the last gear, driving in a straight road. Since the engine is coupled to the wheels at a fixed ratio (the fifth gear's ratio), RPM is proportional to the speed you are going. Under these assumptions, the fuel used per distance traveled would be proportional to the throttle, and so pressing the gas pedal the least would result in a better mileage. Am I missing something?


If your last gear has a gear ratio of 1 (mine is 0.7), yes that's true. The optimum place for fuel efficiency depends on the torque output of the car.

Horsepower is directly proportional to torque and rpms, so you need to know the torque to know where the most optimal fuel efficiency is
with a given range. Say in your hypothetical car, your torque is 100 newton-meters at 1000 rpm. Then let's say it's 200 newton-meters at 1200 rpm.

This is absurdly unrealistic, but in this case you'd probably be more fuel efficient at 1200 rpm than 1000 rpm. Per unit of fuel, you're putting out more power
overall. If instead torque was monotonically decreasing (never increasing) from say, 1000 rpm to redline, then 1000 rpm would be the most optimal for fuel efficiency.

tl;dr:

- Fuel economy depends on the torque output of the engine.
- Torque varies by engine.
- Optimal fuel efficiency will not always be at the lowest rpm.

Other notes:
Spoiler:
I've wondered about this for a while and I started working on a simulator for basic engine. I wanted to know the peak fuel efficiency for my car,
but fuel efficiency as a function of throttle and gear is a highly nonlinear function. There's lots of local maxima and you need to know the complete
torque curve, aerodynamics of the car, losses from utilities (which can be neglected for a first order approximation) and the rolling resistance
present in the wheels.


moiraemachy wrote:
Zamfir (emphasis mine) wrote:Of course, if you do not press the pedal, the engine will consume the least amount of fuel. Namely zero.


Is this the case? I'm pretty sure most modern engines can keep on running indefinitely when the gas pedal is not pressed, which would not happen if there was no fuel intake. I assumed that the throttle valve would always let some air in.

Also, sorry for kind of hijacking the thread OP. :oops:


Technically the fuel consumption isn't zero. The engine still needs to keep spinning to prevent stall, so it's going to consume some tiny amount of fuel
to maintain the idle speed. The more utilities you have turned on, the higher this idle speed is because they're all putting a load on the engine for power.

Do you hear your engine making noise when you're parked with the car started? It's consuming gas. If it wasn't, we'd have perpetual power.
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Re: RPM vs Gas Consumption

Postby TrlstanC » Thu Jan 19, 2012 5:27 pm UTC

Izawwlgood wrote:Could someone clarify something here:
RPM is a measure of how hard the engine is working.

...

The gas pedal is only influencing RPM. Right?


Not quite, it's generally true that RPM is pretty much proportional to output, but it's not a hard and fast rule. Horsepower is the measure of how hard the engine is working, and horsepower is proportional to RPM and Torque. When we're measuring the output of an engine everything is defined in terms of rotational work, but it's also possible to think of it in linear terms (pistons move straight down, the car moves straight forwards). How much torque the engine is generating is a measure of how hard the combustion gases are pressing down on the pistons. If you look at a graph of torque vs RPM for most engines it looks pretty flat i.e., mostly the same at all RPM rates, but most engines increase slightly as RPMs increase, and then dip down towards the max RPM of the engine. The engine is able to suck in air and combust it with fuel slightly more efficiently at higher RPMs.

Horsepower is proportional to Torque x RPM, so it increases proportional to RPM, but because the Torque curve isn't completely flat horsepower isn't a straight line either, it will hit a peak (usually a little bit before max RPM) and then dip down towards the end.

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Re: RPM vs Gas Consumption

Postby Sagekilla » Thu Jan 19, 2012 5:27 pm UTC

Izawwlgood wrote:Could someone clarify something here:
RPM is a measure of how hard the engine is working. Nothing more, nothing less. So 'efficiency of travel' is a separate metric entirely. So, if you have one car driving uphill on tiny wheels, maintaining at, say, 4000 RPM, and the same car driving downhill on larger wheels, maintaining 4000 RPM, the second car will travel further on the same amount of gas.

The gas pedal is only influencing RPM. Right?


RPM is a measure of how fast the engine is spinning. How hard the engine works depends on the engine in question.
You need to know the torque output to know how hard it's working. Some engines actually drop off slightly as you approach
their redline (for various reasons), meaning they're putting out less power.

w.r.t. wheel size: By introducing a different wheel size, you're effectively changing the gear ratio. If you had constant angular
velocity being applied to a wheel, varying the wheel size won't change the distance traveled. If you start with one wheel size,
and move up in size then the rotation rate of the wheel will decrease to compensate. Likewise, if you move down in wheel size
then the wheel spins faster. In all cases, the total distance traveled is the same.

Your instance has no net change in fuel efficiency. Going uphill and downhill you encounter the same amount of rolling resistance.
Smaller wheel size uphill just means they "spin" faster. But the car still experiences the same rolling resistance per unit distance.
Downhill, if the car is given the same starting velocity as when it had going uphill, it converts potential energy into speed downhill.
Larger wheels means they rotate slower, but they still cover the same distance so you're still experiencing the same frictional losses.

tl;dr: Wheel size doesn't matter.
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Re: RPM vs Gas Consumption

Postby Izawwlgood » Thu Jan 19, 2012 5:30 pm UTC

My confusion is that the original question wasn't about output or efficiency, but about gas consumption at a specific RPM. Maintaining RPM between two equivalent cars, irrespective of actual distance traveled, means gas consumption is also the same.
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Re: RPM vs Gas Consumption

Postby Sagekilla » Thu Jan 19, 2012 5:35 pm UTC

Izawwlgood wrote:My confusion is that the original question wasn't about output or efficiency, but about gas consumption at a specific RPM. Maintaining RPM between two equivalent cars, irrespective of actual distance traveled, means gas consumption is also the same.


Only if they're in the same exact gear. If you have two cars in different gears, they need different amounts of throttle to maintain the same RPM.
So just because they have the same RPM doesn't mean their throttle is at the same position.

Fuel consumption is directly proportional to RPM and throttle.
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Re: RPM vs Gas Consumption

Postby Izawwlgood » Thu Jan 19, 2012 6:11 pm UTC

Throttle controls RPM though, right? So saying 'maintaining throttle' is like saying 'if RPM remains the same'.
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Re: RPM vs Gas Consumption

Postby JBJ » Thu Jan 19, 2012 6:20 pm UTC

Izawwlgood wrote:Throttle controls RPM though, right? So saying 'maintaining throttle' is like saying 'if RPM remains the same'.

Throttle controls RPM, but different amounts of throttle will have different effects on RPM depending on the load.

Easy way to demonstrate. With a car in neutral/park (no load), give it a bit of throttle. Just a tiny, tiny, tiny bit. When you give it just a little bit of throttle, it revs really high, really fast. You can probably red line the engine before you even make to half throttle on most cars. Compare that to when you engage the car in gear (with load). Give it the same amount of throttle you did with no load, and the RPMs will top out at a much lower level.

The same thing happens as you progress through gears. With the engine at half throttle, in first gear it may rev up to 6000 rpm. In second gear, the same throttle setting would get you to say, 4000 rpm. In third gear, 3000, etc... (depending on the gear ratios).
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Re: RPM vs Gas Consumption

Postby Izawwlgood » Thu Jan 19, 2012 6:24 pm UTC

Right, but the question wasn't about load. The question was if constant RPM was maintained, then two identical cars will consume equal amounts of gas, even though one may have traveled further.
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Re: RPM vs Gas Consumption

Postby TrlstanC » Thu Jan 19, 2012 6:39 pm UTC

The amount of power an engine can generate is constrained by two things: 1) how big it is (how much room there is to squeeze air and fuel in it) and 2) how fast it can get air and fuel in to that space. The space (displacement) is fixed for a particular engine and fuel is easy, modern engines can squirt in wayyy more fuel than the engine can possibly use; the big limitation is how fast can the engine suck in air. While the engine is sucking in air, a bunch of things are measured (volume, temp, etc.) to figure out how much Oxygen there is in that air. The goal is usually to have a mass of oxygen about 14x the mass of fuel, so the car figures out how much air (and therefore O2) is going in to the cylinder and squirts in the correct amount of fuel.

If you have two identical engines, in the same environment then a lot of the factors that determine how much air gets sucked in to each cylinder on each revolution will be the same (air pressure, temp). If the load on the two engines (how much resistance there is to it turning) is the same, if you open up the throttle the same amount they'll spin at the same RPM.

Now imagine that the two engines have different loads on them, one has almost no resistance to spinning and the other has a resistance equal to say 50 horsepower. You can still get both to spin at the same RPM, the low resistance engine will have its throttle mostly shut, and the high resistance engine will have its throttle part way open. In theory they would both be sucking in the same amount of air, and adding the same amount of fuel, the fuel consumption per revolution of the engine would be the same. If they were spinning at 10 or 100 RPM they probably would be. But in reality, when they're spinning at 3,000 RPM the engine with the partly open throttle is able to suck in air a little more efficiently. Even though the volume to be filled, and the speed of the piston in the cylinder is the same, the fact that one is pulling air in past a tiny crack while the other has a clear(er) pathway means that the one with the open throttle actually ends up with slightly more air in its cylinder every revolution. The car measures this and squirts a little bit more fuel in to burn properly.

The clearest example of this is when a car is getting its power measured on a Dyno, they'll do a few runs in different gears and the output of the engine will be slightly different in the different gears (and therefore at different throttle positions at each RPM). The difference in power is due to small differences in the amount of air (and therefore fuel) that can get in to the cylinder when the throttle is at different positions, even at the same RPM.

Honestly, I don't understand the fluid dynamics of the column of air rushing though the intake, past throttles and valves that are slamming open and shut hundreds of times a second to have any guess about which RPM would be the most efficient, or what all the many interactions are that cause the differences. And I'm sure that just driving around I'd never be able to tell what kind of Fuel/RPM efficiency I'm getting. But when you look at the dyno charts there's a clear difference in power/work at the same RPM in different gears. Here's a good example, there's about a 10% difference in work/power depending on gear:

http://www.triplezeecycles.co.nz/Dyno%2 ... harts.html
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Re: RPM vs Gas Consumption

Postby gmalivuk » Thu Jan 19, 2012 6:40 pm UTC

Izawwlgood wrote:Right, but the question wasn't about load. The question was if constant RPM was maintained, then two identical cars will consume equal amounts of gas, even though one may have traveled further.
And the answer to that question was "no".
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Re: RPM vs Gas Consumption

Postby moiraemachy » Thu Jan 19, 2012 6:58 pm UTC

Sagekilla wrote:If your last gear has a gear ratio of 1 (mine is 0.7), yes that's true. The optimum place for fuel efficiency depends on the torque output of the car.

Horsepower is directly proportional to torque and rpms, so you need to know the torque to know where the most optimal fuel efficiency is
with a given range. Say in your hypothetical car, your torque is 100 newton-meters at 1000 rpm. Then let's say it's 200 newton-meters at 1200 rpm.

This is absurdly unrealistic, but in this case you'd probably be more fuel efficient at 1200 rpm than 1000 rpm. Per unit of fuel, you're putting out more power
overall. If instead torque was monotonically decreasing (never increasing) from say, 1000 rpm to redline, then 1000 rpm would be the most optimal for fuel efficiency.


If you assume that fuel_consumption_rate (in, say, gallons/hour) = throttle * RPM, that still does not explain why a car at fifth gear, gas pedal not pressed, steady at 15mph is not the best mileage scenario. (even though it might not have the best energy/gallon efficiency from the engine's viewpoint)

What I am trying to say here is that asuming:

fuel_consumption_rate = throttle * RPM
speed = RPM / gear_ratio

We get

mileage (in km/gallon) = 1/ (gear_ratio * throttle)

Which makes me conclude that either the fuel consumption formula or the claim that the best mileage is obtained at 50-60mph (a situation in which the gas pedal is certainly pressed) is wrong. My guess is that fuel consumption per revolution, at the same throttle, decreases with RPM, but total fuel consumption still increases with RPM.

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Re: RPM vs Gas Consumption

Postby JBJ » Thu Jan 19, 2012 7:25 pm UTC

moiraemachy wrote:Which makes me conclude that either the fuel consumption formula or the claim that the best mileage is obtained at 50-60mph (a situation in which the gas pedal is certainly pressed) is wrong. My guess is that fuel consumption per revolution, at the same throttle, decreases with RPM, but total fuel consumption still increases with RPM.

Because this still ignores power. Engines produce a different amount of power at different RPM. The sweet spot of an engine is the one that produces the most amount of power from the least amount of fuel. This is referred to as specific fuel consumption, and is flow rate/power. Most engines have this sweet spot somewhere in the 2000-3000 RPM range, which coincides with top gear ratios in the 50-60mph range, which is also pretty much by design as that is the typical highway speed.
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Re: RPM vs Gas Consumption

Postby gmalivuk » Thu Jan 19, 2012 7:30 pm UTC

moiraemachy wrote:If you assume that fuel_consumption_rate (in, say, gallons/hour) = throttle * RPM
That equation doesn't say anything directly about how much gasoline is in the cylinder during each revolution, and as such isn't directly the fuel consumption.
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Re: RPM vs Gas Consumption

Postby Yakk » Thu Jan 19, 2012 7:31 pm UTC

moiraemachy wrote:That's precisely what puzzles me: suppose the car is at the last gear, driving in a straight road. Since the engine is coupled to the wheels at a fixed ratio (the fifth gear's ratio), RPM is proportional to the speed you are going. Under these assumptions, the fuel used per distance traveled would be proportional to the throttle, and so pressing the gas pedal the least would result in a better mileage. Am I missing something?

If you take your foot off the gas, your car decellerates, and you are no longer going at the same speed.

So yes, for an instant, your fuel efficiency goes up as you stop using (more than a trivial amount of) gas.

Fuel efficiency over a non-trivial distance is, however, not going to be very high in this case, as your car will drift to a near stop, at which point it will continue to consume fuel while barely moving.

In order to maintain your speed (and the engine RPMs), you will have to press down on the gas pedal.
that still does not explain why a car at fifth gear, gas pedal not pressed, steady at 15mph is not the best mileage scenario
Your car stalls and dies? Which results in not very good fuel efficiency (over a non-trivial distance), because you keep having to start your engine up, put it back into gear, stall it, and repeat.

Few (traditional gas) cars can idle indefinitely in 5th gear.
gmalivuk wrote:That equation doesn't say anything directly about how much gasoline is in the cylinder during each revolution, and as such isn't directly the fuel consumption.
The amount of gas in the cylinder isn't basically a linear function of throttle? (I could see it being far from linear, I'm just curious)
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Re: RPM vs Gas Consumption

Postby Sagekilla » Thu Jan 19, 2012 7:42 pm UTC

Few (traditional gas) cars can idle indefinitely in 5th gear.
gmalivuk wrote:That equation doesn't say anything directly about how much gasoline is in the cylinder during each revolution, and as such isn't directly the fuel consumption.
The amount of gas in the cylinder isn't basically a linear function of throttle? (I could see it being far from linear, I'm just curious)


Basically. The amount of fuel injected depends on a number of factors, plus you have ECM that might vary things depending
on the conditions.

When I say "Fuel Consumption ~= RPM * Throttle", what I'm saying is that increasing either will increase fuel consumption, no
matter what. There's an implicit dependence in there on many other factors.

At the most basic level, there are two things you can adjust your fuel consumption throttle and gear. But it's not linear in
either. Increasing throttle by some small amount doesn't increase the RPM by a proportional amount. You need to take
into account the load present (due to frictional losses, drag, etc) and the torque output of the engine at a given RPM.

Really it's most accurate to say that:
Fuel Consumption = f(Throttle, Gear Ratio, RPM, Speed) ~= RPM * Throttle

RPM depends on the torque, which in turn depends on the load, throttle and gear ratio. The speed depends on gear ratio and
torque. Things get really messy if you try to account for everything. If anyone actually wrote out the equation, it would be an
implicit equation at best.

To answer the original question:

Two equal cars running at equal RPMs but different speeds different gears over equal terrain will consume the same gas.


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Re: RPM vs Gas Consumption

Postby TrlstanC » Thu Jan 19, 2012 8:04 pm UTC

I was just doing some reading on Dynos (prompted by the image I found above) and it looks like a lot of the difference in power at different gears is due to the way the most common kind of dyno measures power (via acceleration). Which would mean that the actual difference in power generated at (and fuel consumption per) RPM would be smaller then shown on that graph. Although the general pattern in the graph, of more power at the same RPM in higher gears, is generally correct.

So, the differences probably aren't as big as assumed, and both intuitively, and even as a first approximation, I'd agree that "same RPM = same fuel consumption" although most likely in the real world you'd see small differences in consumption based on how the engine was tuned.

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Re: RPM vs Gas Consumption

Postby moiraemachy » Thu Jan 19, 2012 8:46 pm UTC

Yakk wrote:
that still does not explain why a car at fifth gear, gas pedal not pressed, steady at 15mph is not the best mileage scenario
Your car stalls and dies? Which results in not very good fuel efficiency (over a non-trivial distance), because you keep having to start your engine up, put it back into gear, stall it, and repeat.


I'll reformulate my point:

Assuming the fuel intake per revolution is not a function of RPM, and that pressing the gas pedal further increases fuel intake per revolution, the claim that cars get their best mileage at 50-60mph does not hold, since by releasing the gas pedal a little and finding a lower stable speed at, say, 40mph would give you a better mileage. For that claim to hold, fuel intake per revolution should go down as RPM goes up. Which kind of makes sense if you assume there's less time for the air to get in, I guess.

Or maybe a car with, say, 30% throttle can idle at 50mph, but would lose speed and stall at 40mph due loss of efficiency? I'm confused.
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Re: RPM vs Gas Consumption

Postby gmalivuk » Thu Jan 19, 2012 9:04 pm UTC

I don't know everything that in fact goes into affecting fuel consumption. I just know that, empirically, most cars have their best mileage at about 50mph.

If other things would seem to preclude this, it's those other things that don't hold or are incomplete.
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Re: RPM vs Gas Consumption

Postby TrlstanC » Thu Jan 19, 2012 9:48 pm UTC

moiraemachy wrote:Assuming the fuel intake per revolution is not a function of RPM, and that pressing the gas pedal further increases fuel intake per revolution, the claim that cars get their best mileage at 50-60mph does not hold,


What pressing the "gas" pedal down does is open the throttle, which reduces the amount of power the engine needs to spend sucking in air. This additional power is then used by the engine to make itself spin faster. There's way too much power generated to just spin engine bits, so we can "use up" the extra by making the wheels spin and the car go accelerate. As the engine spins faster, and the car goes faster, resistance to acceleration increases and eventually there's no more power "left over" from the engine (from spinning itself around and sucking in air) the car comes to a steady speed for this amount of throttle and gear selected.

So, as RPMs increase a few counter acting things are happening:
1. The engine bits are spinning around more, this uses up power i.e. burnt fuel. But it also takes up a smaller and smaller percent of the total power created.
2. The engine pumps more air in, and it becomes more efficient at pumping in air (at least up to a point, I assume engines are tuned for peak pumping efficiency at common RPM levels)
3. MPH increase, and resistance (most at higher speeds) increases

What the balance between these three things means is that neither very low nor very high speeds are best for MPG (which wasn't the original question, but is still relevant). The most efficient speed will be the one where the engine is "breathing" the most efficiently (generally higher) while also spending the lowest amount of energy on spinning itself (also generally higher) and the lowest amount pushing air out of the way of the car (always lower).

Well, it’s probably more accurate to say that engines burn fuel to make heat that is then discarded in to the atmosphere, and that there’s a little physical energy left over that happen to move some things around…

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Re: RPM vs Gas Consumption

Postby Hawknc » Fri Jan 20, 2012 8:27 am UTC

gmalivuk wrote:I don't know everything that in fact goes into affecting fuel consumption. I just know that, empirically, most cars have their best mileage at about 50mph.

If other things would seem to preclude this, it's those other things that don't hold or are incomplete.

The bits not mentioned there are "most vehicles get their best mileage at about 50mph when in the expected gear, on straight and level road with no wind load". If you're the kind of person who holds gears or you typically switch from first to fifth, you may find differently.

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Re: RPM vs Gas Consumption

Postby Zamfir » Fri Jan 20, 2012 11:27 am UTC

moiraemachy wrote:I'll reformulate my point:

Assuming the fuel intake per revolution is not a function of RPM, and that pressing the gas pedal further increases fuel intake per revolution, the claim that cars get their best mileage at 50-60mph does not hold, since by releasing the gas pedal a little and finding a lower stable speed at, say, 40mph would give you a better mileage. For that claim to hold, fuel intake per revolution should go down as RPM goes up. Which kind of makes sense if you assume there's less time for the air to get in, I guess.

Or maybe a car with, say, 30% throttle can idle at 50mph, but would lose speed and stall at 40mph due loss of efficiency? I'm confused.

The answer is loss of efficiency. As people above already mentioned, low throttle is bad for efficiency. There will be a lot of air friction when the air flows through the small opening, and that's energy that your engine has to produce but won't be able to use for driving.

So if you reduce throttle and drive at a lower speed, then fuel consumption in liter/second goes down, but it does not go down linearly with speed. At low speeds and low throttle settings, lowering the throttle further will reduce efficiency a lot. You will still consume less fuel per second, but your speed (in meters/second) goes down faster than that. So fuel consumption per meter will go up.

If you can shift to a higher gear, you're golden. Then the engine runs at lower RPM but higher throttle, so efficiency is high again. But if you're already in maximum gear, you get better mileage when you go a bit fast then going as slow as possible.

That's part of the trick of hybrid cars: if you drive at a low-throttle speed, the car will either drive on the electric engine, or turn the gasoline engine at an efficently high throttle setting and store the excess power in the battery.

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Re: RPM vs Gas Consumption

Postby moiraemachy » Fri Jan 20, 2012 2:21 pm UTC

Yeah, that makes sense. Thanks folks.

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Re: RPM vs Gas Consumption

Postby JBJ » Fri Jan 20, 2012 3:13 pm UTC

Here's why cars do best at 40-60mph

The first thing to understand is that for any given RPM, the power output of the engine is related to how much throttle it is given. If you look at a Dyno graph, that torque and HP curve is the maximum amount of power at those RPMs. The Dyno graph is generated by running the engine at wide open throttle. At 3000 RPM, the amount of HP produced by the engine can be, say, 100HP at full throttle or 30HP at 50% throttle. Notice I didn't say 50HP, it's not a linear relationship.

Now, take a look at this chart, a brake specific fuel consumption graph:
Spoiler:
Image

You'll notice the data points along the top is the torque curve. That is this engine's maximum torque for the RPM. There's no formula that can predict this chart. It has to be created by actually testing the engine. Every engine is different, but they all look very similar. They will all have that island in the middle (this one labeled 250). That is this engines specific fuel consumption which is 250 grams of fuel per kilowatt-hour. The lower the number, the more efficient.

We're going to look specifically at 2500 RPM where that island is. That is the efficiency sweet spot. The center of that island is the peak efficiency which occurs at right around 2500 RPM and the engine generates 124.8 Nm if force. Converted to foot-pounds of torque, that's 87 ft-lb. Converted to HP (T x RPM / 5252), it's 41.5 HP. That's the most amount of HP for the least amount of fuel that the engine can produce.

The vertical axis roughly represents the amount of throttle applied. At 2500RPM, the sweet spot is at about 70-80% throttle. Nearly all engines have their sweet spot around 2000-3000 rpm at around 75% throttle +/- 15%. For instance, my truck (which is designed to have more low-end torque) has a sweet spot around 1800RPM at ~65% throttle.

Remember, fuel efficiency (in terms of fuel consumption) needs to be measured as fuel used per power produced. This is the reason why: A car will always accelerate to a speed where the power output by the engine is equal to the forces acting against it. There are 3 forces opposing that acceleration.

1 - Internal friction. This is the force required to keep the engine rotating. Cylinder and exhaust pressure, belts and pulleys, alternator, etc... This is a constant force and has no relation to speed.

2 - Rolling resistance. Friction with the ground. This force has a linear relationship to speed.

3 - Aerodynamic drag. This is the force of wind against the car. It goes up with the square of the speed. To go twice as fast takes 4 times the power. The two components of this force (besides speed) is the coefficient of drag (Cd) and frontal area (A). Most cars have roughly the same frontal area and a Cd of 0.3 - 0.4. This means that they aren't really impacted by air resistance until they hit about 30-40 mph. The lower the Cd and A, the higher speed before it becomes an issue.

Technically, there's a 4th force; gravity. However, because this can be both an opposing force (going uphill) or an assisting force (downhill), I'm just going to ignore it and assume we're talking about a level surface.

Now, if we know the engine's most efficient consumption/power speed (in this case, 41.5HP @2500RPM with ~75% throttle), we can work out it's optimal speed for best MPG. We just have to figure out the forces acting against it.

First, internal friction. This is going to be about 2HP. It's roughly the same for most cars and it's constant whether the car is sitting still or going 90mph.

Next, rolling resistance. Also varies by car, but a decent approximation is about 1/4HP for every mph. This goes up linearly.

Finally, air resistance is figured. For a typical car, it takes 1HP to overcome air resistance at 10mph. That's just a rule of thumb, but it's a decent approximation. It also makes it easy to calculate.

So, for a typical car, the following is the total HP needed to reach certain speeds. Rough approximation.
IF - internal friction
RR - rolling resistance
WR - wind resistance

Code: Select all

Speed   IF    RR    WR   TOTAL HP
10      2     2.5   1    5.5
20      2     5     4    11
30      2     7.5   9    18.5
40      2     10    16   28
50      2     12.5  25   39.5
60      2     15    36   53
70      2     17.5  49   68.5
80      2     20    64   86
90      2     22.5  81   105.5
100     2     25    100  127
110     2     27.5  122  151.5

Having previously determined the optimal HP at 41.5, we see that it comes in at just above 50mph. Engineers designing the car will arrange the final gear ratio so that the optimal engine speed (2500 RPM) results in a speed of just over 50mph with the engine producing 41.5 HP.
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