On page II.333 in figure P18.70 in connection with exercise 70 the claim is that 5 m/s of ambient true airspeed produces 20 m/s of airflow in the space between the two trucks, which in turn causes a force pulling them together.
Where does this 20 m/s number come from? Why do you think the air would do that? Intuition?
I reckon my intuition about fluid dynamics is better than most people's ... but I know enough not to trust my intuition. So I did the experiment. I fired up a small wind tunnel with a couple of model trucks. Over a wide range of conditions it was quite difficult to find any reasonable geometry where there was a force pulling the trucks together. Mostly they were forced apart. The only geometry where they were forced together was a forward-pointing wedge arrangement ... but that hardly counts, since in that geometry the left truck was forced to the right even in the absence of the other truck, and the right truck was forced to the left even in the absence of the other truck, just due to the natural shape of things and the nonzero angle of attack ... and in any case that geometry is not consistent with the diagram in the book.
To repeat: In cases where the angle of attack was zero, the trucks were forced apart, not forced together.
FWIW the result agrees with my intuition. Surely you suspected that, because I would not have bothered to do the experiment unless I was already highly skeptical of the claims in the diagram. The successful intuition goes like this: Consider the _circulation_ about each truck. The diagram shows a CW circulation around the left truck, and a CCW circulation around the right truck. That's implausible, to say the least. What could possibly give rise to such a circulation? Starting from the symmetrical zero-circulation case, there is more friction in the gap than there is on the outside, and one would expect that to set up a circulation opposite to what is shown in the diagram.
One way I could come up with the situation in the diagram is by some sort of wacky superposition argument : fast air to the left of the right truck plus fast air to the right of the left truck makes doubly-fast air. However, fluid dynamics doesn't work that way, The equations are waaaay too nonlinear to permit that sort of superposition.
This whole problem looks like flagrant equation-hunting to me: Here's a velocity, here's a density, plug into the formula and turn the crank. The students don't even need to go to the trouble of looking up the density of air.
Real-world data on the average sideways force between conveyances (in a slightly different geometry) is more than an order of magnitude less than what you would calculate based on the equation-hunting / plug-and-chug approach. See e.g. figure 10 in:
http://www.altairhyperworks.com/html/en-us/rl/ACUSIM/papers/Train-Aero-Paper.pdf
This reconfirms my intuition that Exercise 70 is nowhere close to modeling the correct physics.
It might be possible to salvage this exercise, perhaps by putting the trucks in an alley between two enormous buildings, so as to funnel air into the gap between the trucks ... but it may not be worth the effort. I'd prefer to see something that was (a) more connected to verifiable physical data, and (b) more focused on reasoning than mindless equation-hunting.
On page II.333 in figure P18.70 in connection with exercise 70 the claim is that 5 m/s of ambient true airspeed produces 20 m/s of airflow in the space between the two trucks, which in turn causes a force pulling them together.
Where does this 20 m/s number come from? Why do you think the air would do that? Intuition?
I reckon my intuition about fluid dynamics is better than most people's ... but I know enough not to trust my intuition. So I did the experiment. I fired up a small wind tunnel with a couple of model trucks. Over a wide range of conditions it was quite difficult to find any reasonable geometry where there was a force pulling the trucks together. Mostly they were forced apart. The only geometry where they were forced together was a forward-pointing wedge arrangement ... but that hardly counts, since in that geometry the left truck was forced to the right even in the absence of the other truck, and the right truck was forced to the left even in the absence of the other truck, just due to the natural shape of things and the nonzero angle of attack ... and in any case that geometry is not consistent with the diagram in the book.
To repeat: In cases where the angle of attack was zero, the trucks were forced apart, not forced together.
FWIW the result agrees with my intuition. Surely you suspected that, because I would not have bothered to do the experiment unless I was already highly skeptical of the claims in the diagram. The successful intuition goes like this: Consider the _circulation_ about each truck. The diagram shows a CW circulation around the left truck, and a CCW circulation around the right truck. That's implausible, to say the least. What could possibly give rise to such a circulation? Starting from the symmetrical zero-circulation case, there is more friction in the gap than there is on the outside, and one would expect that to set up a circulation opposite to what is shown in the diagram.
One way I could come up with the situation in the diagram is by some sort of wacky superposition argument : fast air to the left of the right truck plus fast air to the right of the left truck makes doubly-fast air. However, fluid dynamics doesn't work that way, The equations are waaaay too nonlinear to permit that sort of superposition.
This whole problem looks like flagrant equation-hunting to me: Here's a velocity, here's a density, plug into the formula and turn the crank. The students don't even need to go to the trouble of looking up the density of air.
Real-world data on the average sideways force between conveyances (in a slightly different geometry) is more than an order of magnitude less than what you would calculate based on the equation-hunting / plug-and-chug approach. See e.g. figure 10 in: http://www.altairhyperworks.com/html/en-us/rl/ACUSIM/papers/Train-Aero-Paper.pdf
This reconfirms my intuition that Exercise 70 is nowhere close to modeling the correct physics.
It might be possible to salvage this exercise, perhaps by putting the trucks in an alley between two enormous buildings, so as to funnel air into the gap between the trucks ... but it may not be worth the effort. I'd prefer to see something that was (a) more connected to verifiable physical data, and (b) more focused on reasoning than mindless equation-hunting.