The physics behind slipstreaming/drafting

[BiteTheDust]

I have been searching all over the internet for information on the physics behind slipstreaming or drafting, such as estimating the optimal distance an object should be behind another in order to experience the least drag. All I have found are a couple of Wikipedia articles as well as short car-racing, biking, and swimming web-pages that briefly cover the subject. If anyone could post any links, resources, or even personal explanations, it would be greatly appreciated.

 

[rcgldr]

For Nascar type racing cars, geting as close as possible is best for drafting, and on the straights, the cars sometimes touch and/or bump, called "bump drafting".

 

[BiteTheDust]

Thanks for the response; however, I think I have found the answer to my initial inquiry in words:

I'm quite sure that decreasing the distance between two trailing objects, whatever shape or size such objects might be, will reduce the force of drag acting on the drafting object (the one at the back). This is due to a decreased amount of fluid particles hitting the drafting object caused by the partial vacuum (lower pressure area) created by the turbulent flow at the rear of the leading object.
Also and surprising for me at first, the leading object's drag is also reduced since the drafting object prevents the fluid from getting as turbulent at its rear, thus reducing the force sucking it back.
If this theory is correct, just like rcgldr stated with Nascar-type cars, the optimal distance between two trailing objects at the same velocity is 0! If they are touching they more or less act like one body, where both objects experience less drag than if they were separate.

As my new question, I'm wondering if there is a mathematical relationship (I'm guessing not linear) between the distance separating two simple objects, such as spheres, moving at the same speed one right behind the other and the drag experienced by the drafting one (this could also apply to the leading one). The velocity of the objects as well as the viscosity and density of the fluid they're traveling in are constant.

If such research has been done on a similar situation as above, does anyone have a link to the paper?
Thanks

 

[cjl]

Honestly, it's hugely dependent on a tremendous number of factors, such as the fluid, the speed, the shape of each object, the size of each object, and even the surface finish (smooth vs rough) of each object. I don't know if any real broad generalizations can be made.

 

[BiteTheDust]

Honestly, it's hugely dependent on a tremendous number of factors, such as the fluid, the speed, the shape of each object, the size of each object, and even the surface finish (smooth vs rough) of each object. I don't know if any real broad generalizations can be made.

I understand this completely and wasn't expecting an equation involving that many factors in anyway. It would be impossible to create a sensible formula that related so many variables.

I was wondering if any tests had been done in a specific environment where some factors are treated as constants. One such case would be in a laminar airflow found in a wind tunnel, where the density, viscosity, and temperature of the fluid (air) are essentially constant. Two simple objects, with constant shape, size, and surface finish would then be set one behind the other in the wind tunnel. Now I understand that velocity is probably the most intricate factor in determining turbulent flow, so let's make that a constant as well: the objects (or more specifically the air particles in the air tunnel) would be always at a speed of 20 km/h. The only two factors that would remain would be what I'm interested in: the force of drag and distance between the spheres.

 

[boneh3ad]

Well for starters, it doesn't really have anything to do with turbulent flow but with the separation bubble and general low pressure region that develops behind the leading vehicle. Turbulent flow would actually lessen the effect because a turbulent boundary layer is much less susceptible to separation than a laminar boundary layer. For example, the reason golf balls are dimpled is to induce turbulent flow, thereby keeping the boundary layer attached longer and decreasing the size of the separated region behind the ball. The smaller region means a much smaller form drag. Of course turbulence comes with a price, namely greater viscous drag and heat transfer, but on a golf ball that is negligible.

Back to the drafting question. Depending on a whole host of factors, there will be a separated region aft of a vehicle that a trailing vehicle can insert itself into to reduce the pressure on the front end of the car. This results in a lower pressure differential between the front and back of the car and lower drag. The size of that separated region, and therefore the drag reduction on the drafter, depends most notably on the shape of the front vehicle. For example, the region of separated air behind a stock car such as NASCAR will be much larger than that behind a Formula1 car.

Even for simple objects an analytical solution would likely be impossible, so experiments or CFD would be needed.

Now I understand that velocity is probably the most intricate factor in determining turbulent flow, so let's make that a constant as well

Velocity is not the only or most important factor, although it is certainly the most simple to understand. It would be correct to hold the velocity constant but not for that reason.

Just for grins, the factors that affect the stability of a boundary layer include the Reynolds number, the shape of the object, the surface finish, the temperature of the object and the fluid, the free stream conditions of the airflow, and more. It is a very complicated process, and one that is not even close to fully understood.

Anyway, I doubt many studies have been done because the results from one shape such as spheres doesn't really have any bearing on other shapes due to all the factors involved. That sort of research wouldn't really help anyone with their driving strategies.

 

[BiteTheDust]

Anyway, I doubt many studies have been done because the results from one shape such as spheres doesn't really have any bearing on other shapes due to all the factors involved. That sort of research wouldn't really help anyone with their driving strategies.

I agree with your reasoning as well. I also had thought of the lack of implications/continuity for an experiment focusing just on spheres, since if we look at more complex objects, the relationship that was determined would mean nothing; I previously believed that it might become a worthwhile stepping stone for future experiments with more variables such as shape and fluid characteristics.

Now that I think of it, research on slipstreaming/drafting may interest scientists since it may have important ramifications in human life other than racing. For example, the price of jet fuel has skyrocketed in the past years and its availabilty is dwindling. An interesting technique researchers are thinking of implementing for fuel economy is changing the design of passenger planes completely in order to fly slower (the physics behind this move is very interesting and I think I will create a thread on it). Also, another concept is having passenger planes follow one other in maybe groups of three to reduce the work needed to achieve lift, and thus reduce fuel consumption; this would be achieved by the two trailing planes flying in the wing-tip vortex of the leading one (just like the V formation many birds use to save energy on long-distance flights).
I know that lift and drag are two separate forces, but planes could use the low pressure area created at the back of another plane in order to reduce drag and fuel consumption even further.
By researching in greater depth the phenomenon of slipstreaming/drafting and its implications for aircraft, physicists could do their part in reducing the greenhouse effect.

In my opinion, even though there are many factors determining the effectiveness of slipstreaming, scientists will eventually find general and even specific relationships between most variables. Since we are in the realm of fluid dynamics, just look at naval architecture: when determining the hull form for a given ship that will travel the fastest while remaining fuel efficient and stable, the quantity of variables that have to be taken into account is astounding (density, viscosity, and flow of water; length, depth, freeboard, draught, and beam of ship; frictional, residuary, and wave-making resistance; drag, lift, and thrust coefficients; wetted surface area, block coeffecient, waterplane area, and Reynold's number; just to name a few ) Even with so many factors to keep in mind, naval architects manage to design fast, efficient, and stable hull forms no matter the needs of the client.

There will be a lot of trial and error as well as very complicated concepts to quantify, but the physics of slipstreaming could become a far-reaching discipline!

 

[BiteTheDust]

Well for starters, it doesn't really have anything to do with turbulent flow but with the separation bubble and general low pressure region that develops behind the leading vehicle. Turbulent flow would actually lessen the effect because a turbulent boundary layer is much less susceptible to separation than a laminar boundary layer.

Thanks for clearing this up for me, but I am still confused on what exactly causes the low pressure region. You say that turbulent flow "doesn't really have anything to do with slipstreaming", while I read that it is the reason for it:

(from wikipedia)
A slipstream created by turbulent flow has a slightly lower pressure than the ambient fluid around the object.

Would this be confusing me since I think of drafting and slipstreaming as the same phenomenon?

The size of that separated region, and therefore the drag reduction on the drafter, depends most notably on the shape of the front vehicle.
...
Velocity is not the only or most important factor, although it is certainly the most simple to understand.

Silly me, of course velocity is not "the most intricate factor" like I previously said. The shape of the leading object, more specifically the front, would be the hardest variable to implement in such an equation. If I understand correctly, this is due to the difficulty to quantify a shape and the complicated effects it has on the lower pressure differential, a.k.a separated region. Please correct me if I am wrong.

Thanks for the informative reply; it has really improved my understanding of drafting/slipstreaming.

 

[boneh3ad]

Thanks for clearing this up for me, but I am still confused on what exactly causes the low pressure region. You say that turbulent flow "doesn't really have anything to do with slipstreaming", while I read that it is the reason for it:

(from wikipedia)
A slipstream created by turbulent flow has a slightly lower pressure than the ambient fluid around the object.

Would this be confusing me since I think of drafting and slipstreaming as the same phenomenon?

The problem with Wikipedia is that anyone can write anything they want on it. Suppose you have laminar boundary layer and a turbulent boundary layer but everything else is held constant. The two would not differ in pressure at a given point except that in the turbulent case, the pressure would fluctuate wildly.

I suppose I should expand my previous answer as well to say that it is more than just a separation bubble. Those can play a big part, but even without separation, there will be a low pressure area behind the vehicle that is commonly called the wake. It won't be as low pressure as a separated region, but it will still be lower than the free stream.

The easiest way to think about the reason for this is that as a vehicle moves through the air, very close to the surface the air must not be moving relative to the vehicle (this is commonly called the no-slip condition). In essence, this means that the vehicle is dragging the fluid with it. This effect persists for a while even after the vehicle passes, meaning a vehicle trailing the first vehicle encounters an area of flow with lower dynamic pressure since it will be moving along with the vehicle to some extent.

A separation bubble would just greatly increase that effect for a short distance behind the vehicle.

Silly me, of course velocity is not "the most intricate factor" like I previously said. The shape of the leading object, more specifically the front, would be the hardest variable to implement in such an equation. If I understand correctly, this is due to the difficulty to quantify a shape and the complicated effects it has on the lower pressure differential, a.k.a separated region. Please correct me if I am wrong.

The front end has much less to do with how the flow leaves the back of the object than the shape of the back end. A sufficiently blunt front end could certainly separate the boundary layer, but that generally won't happen with any shape that anyone uses for a vehicle for precisely that reason. There are very few times where the boundary layer is intentionally allowed to separate, for example on a reentry vehicle of a spacecraft . They let that separate so that they can increase the drag and therefore the aerodynamic deceleration.