Aerodynamics Research on Vehicle Modifications

[Christ]

Originally Posted by RobertSmalls

Similitude (model) - Wikipedia, the free encyclopedia

You can get a dime to float in a glass of water, but a manhole cover the shape of a dime can not be made to float. Surface forces do not scale the way you might think.

If you test a scale model in a wind tunnel without achieving similitude, you will get different results.

If the manhole cover's size and weight were both scaled accordingly to the dime, I'm pretty certain it would float.

The problem with the comparison is that while a manhole cover might be 1,000x the volume, it's probably 10,000x the mass, making it less buoyant.

I do agree about the wind tunnel comparison, though. The changes in cd won't be scalar as the size of the object (and the size of features related to the object) increases.

[RobertSmalls]

Nope! Suppose the manhole cover has a diameter 100 times that of the dime. Its circumference is 100 times as large, and so is the force of surface tension. But the manhole cover is 100 times as thick, too, so its volume is 10000 times as large. The density is the same in this example, so mass, weight, and even buoyant forces are 10000 times as large.

Surface forces scale with L^2, while body forces scale with L^3.

The cross-sectional area of muscle and bone scales with L^2 while mass scales with L^3, which is why an elephant can't jump five times its height like a cat, and why we don't see large animals with the proportional strength of an insect.

[Christ]

dime = approx .5" dia. x100 = approx 50" dia (manhole cover)

dime = .196 area x100 = 19.6" area (manhole cover) right? Wrong. 1,963.5" circ.

dime = 1.57" circ x100 = 157" circ (manhole cover).

Since area is a surface calculation, and it just seems to have scaled to 10,000 times, I'd say there's still something wrong with the analogy.

If the manhole cover had the same density as the dime, but 10,000 times the surface area, and only increased spatial dimensions by 100 times the mass, it would float.

The point is that the manhole cover wouldn't be able to float not because of scaling, but because of the difference in density between the two materials.

Buoyancy is described as the force opposing an objects weight in a fluid because of displacement of said fluid. If the object displaces a weight of fluid that is equal to it's own weight, it will float. On the whole, the object has less mass than the mass of the fluid it displaces. If a manhole cover really had 10,000 times more surface area and only 100 or even 1,000 times the weight, it would also float. Even if it had 10,000 times the surface area and 10,000 times the weight, it would still have the potential to float (provided that you could make a dime float, which I don't recall ever having seen), with the exception of breaking surface tension due strictly to sheer size.

Since surface tension relies on molecules' ability to stick together under strain, a much larger object would have more of a tendency to break surface tension because it would require a much larger group of molecules to cooperate.

[RobertSmalls]

The kind of "floating" I'm talking about here is not buoyancy, it's a result of surface tension. No metals float buoyantly in water, but it's easy to get a paper clip to sit on the surface of water, and it's possible to get a dime to do the same. However, make the dime or the paper clip 10 times as long, 10 times as wide, and 10 times as thick, and its behavior will change.

The point is scale models do not behave the same as full-sized objects, because area and surface forces scale with L^2, while body forces scale with L^3.

[MetroMPG]

Originally Posted by tasdrouille

Basically, what you'll get putting a 1:18 scale model in a wind tunnel with 60 mph airspeed will not scale properly for a full size model at 60 mph airspeed.

Correct me if I'm wrong, but doesn't scale model testing take Reynolds into consideration by increasing the fluid flow proportional to the model?

I thought I'd read that if you use for example a 1/2 scale model, you would double the fluid flow to achieve comparable full scale fluid properties.

[RobertSmalls]

Hmm, yes, I did overlook that. You could preserve the Reynolds number of a half-scale model by doubling the airspeed, but it would become problematic for a 1:18 model of a car. It would take air at 1080mph, or Mach 1.4, to mimic the full-sized car at 60mph, and I don't know whether approaching or exceeding the speed of sound invalidates the results. However, if you use water, which is 50 times as viscous, you can run the 1:18 model at 22mph. A 6"x6" water channel flowing at 22mph (or maybe 11mph is good enough) is relatively easy to build.

However, for an Honors project, I think ignoring but acknowledging the lack of dynamic similitude is sufficient. Unless you want to play with your ME department's water trough.

[Christ]

Originally Posted by RobertSmalls

The kind of "floating" I'm talking about here is not buoyancy, it's a result of surface tension. No metals float buoyantly in water, but it's easy to get a paper clip to sit on the surface of water, and it's possible to get a dime to do the same. However, make the dime or the paper clip 10 times as long, 10 times as wide, and 10 times as thick, and its behavior will change.

The point is scale models do not behave the same as full-sized objects, because area and surface forces scale with L^2, while body forces scale with L^3.

Gotcha. I wasn't clear on exactly what point you were making, and I obviously took the wrong part of the post.

[tasdrouille]

Yes, you are right, but they often test 1:2 or 1:3 models.

Originally Posted by MetroMPG

Correct me if I'm wrong, but doesn't scale model testing take Reynolds into consideration by increasing the fluid flow proportional to the model?

I thought I'd read that if you use for example a 1/2 scale model, you would double the fluid flow to achieve comparable full scale fluid properties.