Aerodynamics ... Opportunities?

[Stan Pope]

It is mostly agreed that on sleek, trim racers that the main aerodynamic losses are caused by the not-very-aerodynamic wheels. In a few circles, folks are trying a variety of fenders to reduce those losses.

I tried a few simulations using Michael Lastufka's simulation program to see what kind of results to expect ... trying to estimate an answer to the question, "Is it worthwhile digging into this further?" The important considerations revolved around the concept that the trailing edge of a fender is critical to achieving benefit. The problem is that a "trailing edge" of a fender is behind the wheel, and to implement it requires moving the rear wheel forward.

For the simulation, I defined four tracks: Four (348") and five section (456") Freedom tracks and four (348") and five section (437") Best tracks. (Start-to-finish distances are estimated from published literature and distant observation. Better estimates and actual measurements would be accepted!)

Then I configured 6 racers:

1. Maximum PE: Basic "extended wheelbase" 1/4" thick racer with the rear wheels flush with the rear of the car. CM at rear axles + 3/8", BSA wheels, Drag coefficient of 0.2.
2. Rear axles at 1": Same car as #1, but wheelbase and CM shifted forward about 0.4".
3. Rear axles at 1", streamlined: Same car as #2, but Drag Coefficient reduced to 0.1. I don't know if 0.1 is attainable. The stubby rear fenders might help some, but enough?
4. Rear axles at 1.4": Same car as #1, but wheelbase and CM shifted forward about 0.8".
5. Rear axles at 1.4", streamlined: Same car as #4, but Drag coefficient reduced to 0.1.
6. Rear axles at 1.4", more streamlined: Same car as #4, but Drag coefficient reduced to 0.05. I don't know if 0.05 is attainable.

Results of the simulated races:
Racer #1 won all four races by about 0.2" (just over 0.001 seconds) on the shorter tracks and 0.1" (just under 0.001 seconds) on the longer tracks.
Racer #3 placed second in all four races.
In three of the four races, Racer #6 trailed the leader by 0.003 seconds. On the short Freedom track, Racer #2 nipped it by a hair (0.014").

My conclusion:
1. Trailing edge fenders on the rear wheels require too much trade-off. Probably not worth digging further. May be worthwhile on the front, though.
2. Other schemes for reducing drag are probably worth the effort. Reducing the drag coefficient from 0.2 to 0.1 seems to buy about 0.4" (short track) and 0.6" (long track) at the finish line. That is a good deal if the drag reduction can be accomplished by other means!

[Stan Pope]

For the Really Obsessive Pineheads (I know who you are so don't be shy!) ... here are the simulation input and output for Freedom Tracks and for Best Tracks. There is (a lot) more detail about the cars and interesting "standings" probes along the ramp and transition.

Enjoy. Maybe even find an error and tell me about it!

[pack529holycross]

If I may ask a few questions, not really having dug too deeply into the physics of Pinewood Derby.....

When simulating "streamlined", does the virtual model take into account the change in the mass of the car near the front wheels due to the addional structure necessary to create said fenders. Or is the model just reducing drag coefficient without consideration for the change in mass, weight distribution, shape, etc?

[Stan Pope]

If I may ask a few questions, not really having dug too deeply into the physics of Pinewood Derby.....

When simulating "streamlined", does the virtual model take into account the change in the mass of the car near the front wheels due to the addional structure necessary to create said fenders. Or is the model just reducing drag coefficient without consideration for the change in mass, weight distribution, shape, etc?

Good question! The model assumes that mass of the fenders were offset by removal of corresponding mass from the car body. For instance, a 0.2 oz fender with its CM 0.25" back from the axle location is compensated by removing 0.2 oz from the car body 0.25" behind the axle. Lateral CM location is not a part of the model and usually not a relevant factor in real life, so that is allowed to change. (Else, I might have to "remove mass where there is no mass.") I also assumed symmetric fenders, so there would be no (theoretical) change to the lateral CM location. Factors like "shape" are combined in the total frontal area and the drag coefficient parameters. I chose the three coefficients as reasonable targets reflecting real life limits.

This is one of the reasons that real world experimentation is messy! Simulation can help cut a lot of strokes off the cases you have to build in wood!

[pack529holycross]

I was curious simply because the "core" or running gear of our cars are pinewood derby slabs, or "skateboards" as we call them, then the rest of the body is balsa grafted on. We do full body mostly, so I was curious about the "fullbody" aerodynamics, as well as the consideration of balsa vs Pine for that portion of the bodies.

[Stan Pope]

Any "additions", pine or balsa or lead or tungsten, are assumed to be rigid and may affect the total frontal area and the drag coefficient. As I understand it, the total frontal area and drag coefficient are "independent". Drag coefficient is based on a unit area and its effect is scaled up (or down) to the actual total frontal area.

In my model, I assumed a negligible change in total frontal area even though I know that if the fender passes above the wheel, it adds to the total frontal area. I excuse my "sloppiness" because the addition to frontal area is quite small as a percentage of the original frontal area.

[pack529holycross]

just wanting to provide some visual inspiration to any wanting to attempt a faired ( fairinged? ) design

[Duane]

I agree that using fenders to fix the air drag problem on rear wheels is hopeless. The main drag occurs downstream of the wheel, and any fairing that kept the boundary layers from separating would require extended teardrop slopes of < 15 degrees, stealing more than an inch from the vital wheelbase and com positioning.

Here's a possible alternative fix to that rear-wheel drag problem. (It probably won't work, but I don't know why yet.)

The main drag effect is from a low pressure area immediately downwind from the wheel. Funnel some air into that void, to get most of it back nearly to ambient air pressure. Using spoilers to deflect air into that void won't work well, because the spoilers would themselves cause wind shadows and negative pressure voids that cause just as much (or more) sucking drag.

But the needed air could be gathered by a scoop further upwind on the car's central body. By putting the scoop an inch or more upstream of the wheel, there is lengthwise room to wrap the scoop in a 15-degree teardrop fairing. That fairing makes the scoop's wind shadow nearly invisible, no matter how big the scoop is or where its air is sent next. The possible tight turns inside the scoop's ducting don't matter much for air drag, as long as the air is accelerating down a smooth slightly-narrowing duct rather than stagnating in an expanding duct.

If the scoop can deliver enough air, with enough pressure, to undo the vacuum downwind of the rear wheels, then the drag from those ungainly wide BSA wheels will get mostly zeroed out. I think the amount of air needed, is equal to the air being blocked by passage of those wheels. So the cross section of the mouth of the scoop(s) should be about the same as the frontal cross section of those 2 wheels combined. Pretty big, and would definitely look weird and exotic.

If this arrangement actually works at all, the main design cost would be in reserving 1/4" space at the rear of the 7" car for ducts to blow into the void behind the wheels. That 1/4" loss would have negligible effect on steering wheelbase and a small effect on gravity potential energy, hopefully balanced by a big win with air drag on longer tracks.

For front wheels, I think lightweight teardrop fairings shaped from paper or thin plastic are the way to go.

[Stan Pope]

(lotsa interesting stuff omitted that I will try to digest fully later) ... For front wheels, I think lightweight teardrop fairings shaped from paper or thin plastic are the way to go.

Rather than a 0.3" wide balsa neutral airfoil with just enough cut out to house the wheel and provide 1/16" ground clearance for the wheel to peek at the track? Not picturing what you are shooting for, though. Elucidate please.

[pack529holycross]

perhaps we can take this conversation to a different hypothetical area of performance gains, although I have a feeling that it might disqualify the car as having more than gravity as an energy source.

Is there enough going on in 32-50 feet at the scale of a 7" pinewood derby car to take advantage of potential energy gains through the application of a venturi type tunnel down the long axis of the car? In reading Bernoulli's principle much of it applies to fluid dynamics, but if I am not mistaken it also is incorporated into the design of jet propulsion engines?

I love posing these types of questions to the thinktank of deep thinkers we have at our disposal here on this forum


The pressure at "1" is higher than at "2" because the fluid speed at "1" is lower than at "2".

more from wiki :

"A de Laval nozzle (or convergent-divergent nozzle, CD nozzle or con-di nozzle) is a tube that is pinched in the middle, making a carefully balanced, asymmetric hourglass-shape. It is used to accelerate a hot, pressurised gas passing through it to a supersonic speed, and upon expansion, to shape the exhaust flow so that the heat energy propelling the flow is maximally converted into directed kinetic energy. Because of this, the nozzle is widely used in some types of steam turbine, it is an essential part of the modern rocket engine, and it also sees use in supersonic jet engines."



Something tells me that this would be more an exercise of presenting a cannard to those who might be fooled into thinking your car is gaining propulsion through such an application, but I have always been curious about the effects in general on wind flow, frontal area, and drag coefficient.

[Stan Pope]

although I have a feeling that it might disqualify the car as having more than gravity as an energy source. ...

Unless you are igniting some fuel I think you are looking for "something for nothing" (usually a hopeless venture), and igniting some fuel would in most venues get your car DQ'ed. Some inspectors might miss it, but the starters would probably sniff it out.

Seriously, I suspect that the drag caused by the front-end air funnel would do the idea in.

You are welcome to demonstrate that I am wrong, however, and the community would be in your debt!

[Kenny]

I've never played with fenders after playing with such questions a few years ago. My conclusion was that the 7 inch body length limit was a problem.

Reading Stan's post makes me wonder what happens if a few standard car limits, i.e. length, or weight, or both, are lifted.

K

[Stan Pope]

Reading Stan's post makes me wonder what happens if a few standard car limits, i.e. length, or weight, or both, are lifted.

K

If length were extended, but rear axles limited to 6.4" from front, then I suspect that rear fenders with "nice" trailing edges would be useful. We could get a measure of usefulness by demonstrating the value of full front fenders, which are within the current limits. That there should be some value is suggested by the occasional replacement of the off-side front wheel with a more aerodynamic "peg."

I suspect that each wheel contributes drag in approximately equal amounts unless the wheels are spaced closely. The front wheels don't, I think, shield the rear wheels from adding drag.

If there were incremental value in fenders for "fat" BSA wheels, then I would think we would see full front fenders more frequently among advanced racers.

[Duane]

For front wheels, I think lightweight teardrop fairings shaped from paper or thin plastic are the way to go.

Rather than a 0.3" wide balsa neutral airfoil with just enough cut out to house the wheel and provide 1/16" ground clearance for the wheel to peek at the track? Not picturing what you are shooting for, though. Elucidate please.

I think a combination of balsa, paper, and stiff plastic sheet would work best.

A clear plastic-sheet removable flap would cover the flat outboard face of the wheel. Has to be clear (for inspection) and easily removed/reattached. Hold down the flap with scotch tape. The plastic I have in mind is the thin stuff used for anti-theft packaging around stuff hanging from stores' hooks. Worked well for dragon wings, last year. (What's that plastic called?) BSA sells a fenders and cockpits kit that is basically just a vacuum-shaped package, without any contents. If we could reshape such stuff ourselves, that would be really great!

The pyramidal wedge downwind of the wheel would be carved from balsa. Then remove unneeded interior wood core by drilling holes sideways. Cover those holes with paper skin. The size of the wedge would be determined by the +3/8" width of the fender, and the 15-degree-or-so slope that can re-merge the airstreams w/o separation of boundary layers. The diameter of the wheel and fender doesn't affect the wedge's length. Only the cross-section's thinnest dimension matters.

The top and front of the fender is basically an outside section of cylinder. Maybe a bent plastic sheet for simplicity and low weight, or a snip from a tin can. Maybe the upwind section is slightly rounded at its edges, like a bicycle fender. Or not. Don't bother with any crossways rounding of the fender above the wheel.

At rear of the car, the body should taper to a blunt knife edge from its thickest points at rear axle and weights. Don't terminate the body with a fat wedge, as is common in many pwd cars.

If the center body of the car has any interior cutouts to save weight, cover over those holes with paper, on top and bottom surfaces. If the front axle area is followed by a necking of the car body, the exposed rearward edges of the front axle should have a teardrop profile. Putting pointy edges on anything pointing into the wind is pointless at these speeds; blunt rounding gives the same lower drag, at less weight.

[Stan Pope]

Well, in a fit of pure cussedness, I asked myself, "What if our 'Daddy Car Class' were limited to 2.5 ounces or, even, 2.0 ounces?" (Still with those "fat" BSA wheels, of course!)

The picture changes a bit. As one might expect, the 0.6" rear-to-axle car not only becomes problemmatic to build, but it also becomes less competitive!

See:
http://stanpope.net/derbytalk/Fenders_B ... Ounces.txt

http://stanpope.net/derbytalk/Fenders_F ... Ounces.txt

http://stanpope.net/derbytalk/Fenders_B ... Ounces.txt

http://stanpope.net/derbytalk/Fenders_F ... Ounces.txt

Does this end the solution's search for a problem that it can solve!