What mass of air?

[ChrisGreaves]

A motor-car is driven at 60 mph in a straight line on a horizontal surface.
What mass of air must be moved out of the way (of the car) per second?
Assume air pressure of 15 lbs/sq inch.
Assume a cross-sectional area of the car of 4 feet high by 5 feet wide with NO ground clearance. That is, the entire mass of air must be pushed aside or over the car, but cannot pass under.

[HansV]

The volume of air displaced by the car is a rectangular box 5 feet wide, 4 feet high and 60/3600 mile long.
Converting everything to metric: 1.52 m * 1.22 m * 26.82 m ~ 49.84 cubic metres.
The specific mass of air at 15 degrees Celsius at standard atmospheric pressure is about 1.2 kg/m^3.
So the mass is ~60 kg or 132 lb.

[Sundog]

the entire mass of air must be pushed aside or over the car, but cannot pass under.

Can't some of the air be compressed in front of the car, instead of being pushed aside or over it? If the car makes a sudden stop, does the 132 lb of air keep on going? How much of it would impact a person standing just beyond the front bumper?

[John Gray]

Doesn't streamlining and laminar flow come into this question somewhere? Cars don't really move a mass of air, but displace it.

[HansV]

Yes, but I fear that's beyond the scope of this forum.

[ChrisGreaves]

Can't some of the air be compressed in front of the car, instead of being pushed aside or over it?

Hi Sundog.
I'm thinking of what it looks like from another car driving (well) behind the subject.
A 5x4=20 sq ft "plate" or piston head is traveling forwards.
For each foot traveled forwards, 20 cubic feet must be moved out of the way.
A mass of air, 20 cu ft in volume must be moved out of the way.
How it is moved is a good question, but that it is moved is undebatable (since the piston is solid steel, with no chance of the air passing through it), so to that first level of thought, Hans's answer is correct.
132 lbs of air has to go somewhere.

[ChrisGreaves]

Doesn't streamlining and laminar flow come into this question somewhere? Cars don't really move a mass of air, but displace it.

Hi John; please see also my response to Sundog.
What's the difference between "move" and "displace"? My Canadian Oxford says for displace 2. Move of shift from its accustomed place.
I agree that streamlining etc. can change the amount of work done to displace the mass of air, but I think that it all starts with a need to move 20 cu ft of air.

Reality sets in and if we stay for a moment with a rectangular piston plate, the fluid will economize its movement to "get out of the way" with the minimum energy. That is, i think it will take the path of least resistance.
For some of the air this might be moving to one side; for some it might be upwards, which means it tries to lift a column of air 20 miles(?) high, not all of which will move vertically, for surely some of that column will displace air sideways.

Somewhere an engineering student must have been asked to model this on a Fortran II program on 80-column punch cards; it's the sort of exercise Daniel D McCracken would have loved.

[John Gray]

I understood from what you were saying that you thought that a volume of air equal to that of the car had to be physically pushed in front of it, whereas I would guess that about 95-99% of the air has to be displaced sideways and upwards as the car passes and then it returns (more or less) to its original position. The aim of the car designer is for the car to do the minimum amount of work, which is why you get all these videos of cars in wind tunnels with smoke trails simply travelling round the car without any turbulence, i.e. that the flow is laminar, as near as possible.

I suspect dealing with this mathematically would be beyond the capabilities of an engineering student. Its close cousin, hydrology, was described to me by a physics lecturer at Oxford as "very complex".

McCracken's book on Fortran IV was much better than the one on Fortran II, IMHO, and I think I still have it in my bookcase. Somewhere...

[ChrisGreaves]

I understood from what you were saying that you thought that a volume of air equal to that of the car had to be physically pushed in front of it, whereas I would guess that about 95-99% of the air has to be displaced sideways and upwards as the car passes and then it returns (more or less) to its original position.

Hi John. No, I wasn't too concerned with "in front of" as much as "somehow got moved out of the way".
I was mulling over work-done by a vehicle, and figured that a first approximation was that a mass of air had to go somewhere. Once the mass is known one could calculate various scenarios, including but not limited to {a} the air pushes a column of air upwards, producing a temporary 20 cuft bulge in the upper atmosphere (causing extra drag on the shuttle ...) {b} the air pushes equal volumes of air directly sideways {c} half the mass goes straight up, a quarter goes to each side and so on. Streamlining is beyond me when I'm trying to do in-head calculations while driving (grin)

The aim of the car designer is for the car to do the minimum amount of work, which is why you get all these videos of cars in wind tunnels with smoke trails simply traveling round the car without any turbulence, i.e. that the flow is laminar, as near as possible.

I quite agree, and I think that within say 100 feet or less of the car, we can consider that the air moves around the car and that air beyond the 100 ft radius is unaffected, despite that butterfly down there in the Amazon.

I suspect dealing with this mathematically would be beyond the capabilities of an engineering student. Its close cousin, hydrology, was described to me by a physics lecturer at Oxford as "very complex".

I don't know, but i rather think that differential equations on an analogue computer (which I studied for 1 week back in 1976(?) might have an answer. I'm sure the Bright Boys at Ford, GM etc have it all down pat. It must be an eternal struggled between what the artists say looks good and what the engineers say works, and I bet the engineers bring numbers to the board room.

McCracken's book on Fortran IV was much better than the one on Fortran II, IMHO, and I think I still have it in my bookcase. Somewhere...

Well of course, you are bound to.
But there again you don't delve into your copy nostalgically every night, do you (huge grin)

[AlanMiller]

Can't some of the air be compressed in front of the car, instead of being pushed aside or over it?

How it is moved is a good question, but that it is moved is undebatable (since the piston is solid steel, with no chance of the air passing through it), so to that first level of thought, Hans's answer is correct.
132 lbs of air has to go somewhere.

I think the best way to look at this is as "before and after" snapshots. Before the car enters the frame, there is a certain volume of air only - initial state. While the car is in the frame, the volume of air is reduced by the volume of the car. After the car is well passed, the situation returns to the initial state. As you say, the dynamics of the situation are irrelevant to your question. It's simply a conservation of volume problem, if you make the frame sufficiently large to blur out effects of local compression and rarefaction of the air.

Alan

[ChrisGreaves]

I think the best way to look at this is as "before and after" snapshots.

Thanks Alan, a good thought-experiment. I think that was a vague feeling in my mind that somehow or another a mass of air had to be moved, and one could evaluate a worst-case energy cost by treating it simply as a volume of air (per second) that had to be moved out of the way.
Several better-than-worst cases can be construed with ideas of streamlining, perhaps, which to my mind really means "where the air is displaced to".
My worst-case might be "displace the volume dead-vertical, i.e. push a square cylinder of air vertically to the height of the atmosphere. Another simple scenario might be "push the volume four feet to one side, and assume no resistance".

[DaveA]

Remember that it is this same movement of air that allows a airplane to fly. The air is directed to the lower side of the wings to give it lift.

This is why on the real fast race cars we have the "Spoilers" to keep them on the ground, the lift is on the upper side and pushes the car down.

[ChrisGreaves]

Remember that it is this same movement of air that allows a airplane to fly.

Quite so, and thanks Dave.
As an aside, I live under a flight path to YYZ Toronto, about 2 miles south of the runway, and still stare in amazement at the tons of metal "floating" over my head each day.

I am in no position to do the fluid dynamics calculations, but driving behind a car am struck with the cross-section of the car that must displace that same area of air, multiplied by distance-per-second.

In my original post I assumed no ground clearance, mainly to avoid the discussion of fluid dynamics (another one of my weak subjects!). It seems to me that the calculation of mass-of-air-moved-per-second has to be a first approximation to the calculation of energy used in moving the car through the air, that is, energy consumed in overcoming air resistance.

[AlanMiller]

Thanks Alan, a good thought-experiment.

If you want to do a real experiment, you could Measure the drag coefficient of your car and use it to calculate the kinds of forces needed to be overcome, to move the car along at 60 mph. The fluid mech side of it is not too hairy for the simplified case - Drag coefficient - Wikipedia, the free encyclopedia and Automobile drag coefficient.

Alan

[ChrisGreaves]

If you want to do a real experiment, ... Measure the drag coefficient of your car

Thanks Alan, but no, I can't afford the equipment. Buying a car would be bad enough, then there's the registration, insurance, gas, ... (grin)
Good site though, and I might give it a try next time I borrow a friend's car.