Aerodynamics of Road Vehicles

A book review by the "Lone Danger" Nick Demma

I will proceed with this book review by presenting a totally unorganized mess of comments. There is a section on drafting where the relative coefficient of drag is presented for both the leading and the following cars as a function of the distance between them. First we consider two poorly streamlined cars that have coefficients of drag (Cd) of .47. As the distance between them decreases from a separation that is twice the car length, the Cd of the leading car falls to 80% of the value that it was without the other car. The Cd of the following car is about 85% at the same initial separation, but it rises to more than 100% when the separation is a bit more than half car length and then it falls to 40% as the distance approaches zero.

Even tailgating idiots do not benefit much from drafting because you have to get extremely close to get the large benefit. Bike riders in a pace line learn to ride with only a couple inches of clearance between the tires and this is why they do this. Now for the shocking news. If we use streamliners that have Cds of only .17, the Cds are 100% for the leading car and 80% for the following car when the separation is 2 car lengths. When the separation is 70% of one car length, the Cd of the leading car has fallen to about 70% and the Cd of the following car has risen to 100%. As the separation approaches zero, the Cd of the leading car falls to 18% (!!!, yes, eighteen) and the Cd of the following car rises to 130%.

This astounding result suggests that you should try desperately to stay in the lead when racing streamliners and that staying in the lead will be quite easy because the following streamliner is doing most of the work. The lead is a good place to be when crossing the finish line anyway. It is as if the leading car is parting the air and then bringing it back together and slamming it right into the nose of the following car, while the bow wave of the following car if filling up the low pressure region that would otherwise cause drag for the leader. These results are so counter-intuitive that I would like some empirical confirmation of this effect from riders in the Human Powered Vehicle (HPV) races. The information about drafting inspires this question: How far away from a streamliner does one have to be in order to initiate a clean pass, without helping the leading streamliner by reducing its drag? For the streamliners that have Cds of .17, here's the table:

	Separation Leader Follower  0.00 18% 125% 0.25 38% 120%  0.50 58% 110% 0.75 80% 93% 1.00  91% 89% 1.25 93% 86% 1.50 95% 85% 1.75  97% 84% 2.00 98% 84%
The separation is the distance compared to the vehicle length and the drag is the percent compared to being totally separated.

This table indicates that you shouldn't let the gap go lower than one vehicle length, so pull out to pass before this happens. The feedback from HPV racers, however, is that this reverse-drafting effect doesn't occur and that you are better off in back, so there is some discrepancy between the wind-tunnel tests and the race track. Maybe we are not achieving the low Cd of .17 due to practicalities like wheels and holes in the fairings. The book covers aerodynamics so comprehensively that you can find plenty of contradictions.

One section describes how adding a hemisphere to the front of a cylinder lowers its drag coefficient from .8 to .2 (more about this later), but another section (page 74) says this: "On the drag problem of a body, it might be mentioned finally that the shape of a body in front of the largest cross-section has only minor influence on the total drag--as long as no separation occurs already there. The main contributions to the drag force originate from the rear part of the body. It is not so important to find a proper shape to divide the oncoming flow but it is very important to design a rear body surface which brings the divided streamlines smoothly together. Optimum shapes are streamlined bodies having a very slender rear part, which is not suited to road vehicles." I suspect that the qualification "as long as no separation occurs ..." is critically important because otherwise it makes it sound like we could ride around in bricks as long as we build nice tailboxes for them. The fact that the drag for the leading streamliner can decrease so much when another streamliner is following it does suggest that the tail is important because it is difficult to imagine how the following streamliner could affect the airflow in the front of the leading streamliner.

This suggests that a Lowracer is in trouble even if it has a nice streamlined shape and a flat bottom. The discussion of ground effects raised the issue of ground clearance for a trike and the influence on drag. On page 394 we have this: "The flow volume between the vehicle and the ground and thus mainly the vertical forces are strongly dependent on the car's attitude relative to the ground. ... Very small ground clearances result in positive lift since there is hardly any airflow between the underbody and the ground. With increasing ground clearance, the airflow in the nozzle-type space between the vehicle underbody and the ground produces low pressures causing overall lift to be lowered to negative values and then to rise again as ground clearance continues to increase. The increase in overall lift is due to the fact that the flow velocity under the car decreases as ground clearance increases, thus reducing the low pressure level. Air drag increases as a function of ground clearance though this increase is smaller by one order of magnitude than that of the lift forces. ...lift variations occur mainly in the nose of the car." The variation of drag with ground clearance is such a weak function that the design should be based on other practical considerations rather than drag. Note that the drag gets lower as the clearance decreases, which contradicts the information presented in the table a couple of paragraphs ago.

 One reason why there is so much confusion over aerodynamics is that there are these effects that reverse directions. Compared to a smooth ball, a dimpled golf ball has more drag at low speeds and less drag at high speeds. The speeds at the golf course are high, so the balls are dimpled. It would probably be better to have a smooth nose and then a trip-wire turbulator if you could control the orientation of the ball during its flight. The book does not discuss the design of NACA ducts or turbulators, although there is discussion about where to put the vents to achieve the desired air flow. This too is complicated and merely leaving a hole in the back of the bike does not guarantee that air will flow out of it.

 The chapter on motorcycles shows two lowracer streamliners from about 25 and 50 years ago. These things look like they belong in the HPV races because the rider position is exactly like the position in contemporary lowracers. When reviewing any technology, it is usually amazing how early there was significant progress that everyone later forgets about.

The book devotes almost as much attention to lift as to drag. Bikes don't go as fast as cars so they do not generate as much lift, but they weigh so much less that lift is even more important anyway. When riding a streamliner in a crosswind, you have to lean into the wind to balance. The shell is then acting like a wing and generating lift. The Easy Racers Bike by Gardner Martin is infamous for crashing at high speeds because of this effect. I have experienced front wheel chatter on my bike. The front wheel becomes airborne and it blows downwind a bit before coming in contact with the ground again. The cycle then repeats with a frequency high enough for the rider to experience it as chatter. Ordinarily, we try to ride while simultaneously remaining upright and controlling the direction of travel. When this chattering starts, you basically have to choose either one or the other of these goals. Instinct for self preservation seems to favor remaining upright because it is the most immediate problem, but the direction of the wind and the location of traffic can make the direction of travel a high priority also. Riding in these conditions is more than moderately disconcerting and it inspires daydreams about trikes.

If we accept the premise that keeping the front wheel on the ground is a worthwhile design goal, then we find the section on nose design interesting. There is a comparison between an up-turned nose (ugly), a bullet nose (symmetrical), and a down-turned nose (ground-hugging). The Cd is worst for the up-turned nose (slightly); the other two are very close. More significantly, the lift is much higher for the up-turned nose. The lift is best (actually negative) for the down-turned nose.

There is one plot that shows the drag for various shapes as a function of the length to width ratio (L/D)of the vehicle. Shapes with completely blunt ends have Cds from about .8 to 1 whether they are round or square in cross section. If the back is left blunt and the front corners are rounded to the point where the front is a hemisphere, the Cd gets down around .2 when L/D is between four and eight. The Cd is not a strong function of L/D as long as L/D is greater than three. The best shape is the one that is rounded on both ends and the taper is so long that there is no middle; half of the shape is nose and the other half is tail. The drag gets down to about .12 when L/D is six. Unfortunately, they don't have the case where the back is square and the front has a long taper, so it is difficult to directly compare the hemispherical nose to the long nose. The difference between the hemispherical nose and the long tapered nose is a difference of only .08, but much of this may be due to the long tapered tail on the best design. Although .08 doesn't sound like much in absolute terms, the difference between .2 and .12 is a drag reduction of 40%, which is quite significant. Earlier I was speculating that longer is better but it is intuitively obvious that eventually the skin friction will cause the drag to go up with increasing length. The plot also has skin friction plotted and the plot of Cd as a function of L/D goes through a minimum when L/D is six for the best shape that has a long tapered nose and tail, so there is the answer.

There is data on how much drag is due to various features on a car. If the baseline car has a Cd of .34, then the Cd rises to .55 when you mount a conventional racing bike on top of the car in an upright position. This effect is already gross, so imagine what the drag would be with a rider on it! Of course, we already know that upright bikes are gross, so there you have it. The mirrors on a car can be responsible for 5% of the drag in spite of their area being nowhere near 5% of the total cross sectional area. These examples illustrate the importance of attention to detail.

There is much interesting information about the aerodynamics of trucks. Large improvements are available by rounding the edges, adding deflectors on the tops of the cabs, and adding side skirts that cover the wheels and the space between them. These improvements greatly reduce the spray on adjacent cars that are trying to pass. With gasoline at ridiculously cheap prices in the USA (yes, $1.50 is still ridiculously cheap), we will continue to lug around these big square boxes until the permanent global energy catastrophe begins about ten years from now. (For information about this, see www.dieoff.org.)

I haven't read much from the chapter on heating and cooling, but I am going to cover my windows with low-e window film. This film looks like a mirror from the outside and it rejects 99% of the ultraviolet light, so I will not need to wear sunglasses inside and the solar heat gain will be reduced enormously. In the middle of summer I may use multiple layers of film. The film will be taped to the outside so that there is little light scattering in the plastic. If the film were on the inside, the light would go through the plastic twice. With the film taped to the outside, I could remove it quickly if I don't get home by the time it gets dark and I can argue with police that it is a temporary installation. On a car windshield, this film would be very illegal in many states.

The plots of Figure 4.126 on page 226 show what happens when a nice streamlined shape of length L is height e above the ground. The drag (Cd) is given as a function of the dimensionless ratio e/L. Let's say the streamliner is 3 meters long so we can put some real numbers on things. The Cd is .058 when e/L is .4, which corresponds to a height off the ground of 1.2 meters. The curve is getting flat at that point, so there is little benefit in going higher. The region that we are interested in is crammed into the left side of the plot and the lowest data point is a Cd of .091 when e/L is .04, which is 12 cm or 5 inches in our example. The slope of the curve at this point is .02 (delta Cd) divided by .1 (delta e/L), which is .02/.3 meters or .00067 per centimeter.

In other words, who cares? If the ideal shape is corrupted by having wheels, the Cd goes up to .14 anyway. The wheels add so much drag that getting higher off the ground at the expense of exposing more wheel is not worth it. We should be careful with this conclusion, however, because the plot doesn't go below the 5 inch clearance. The next figure (4.127) has more data at lower clearances and the data came from a difference source. Apparently they had a different shape (more blunt) because they are saying that the Cd is .25 when e/L is .041. Here's the table:

This agrees with some other plots that show the drag going up almost exponentially as the clearance approaches zero. There are curves that don't show this but this is because they don't have data at low enough clearances. From the table we can conclude that:

• A reasonable clearance of 2.7 inches will have low enough drag.
•  Increasing the clearance from this point will not reduce the drag much and the drag may go up because more wheel is exposed.
• Decreasing the height below a half inch is undesirable because of drag and practical considerations.
• We should spend less time worrying about Ground Clearance Vs Drag and more time riding.

There are plots that show the drag and lift forces as a function of the angle of attack. Figure 4.127 on page 226 has plots of the drag and the lift for three different ground clearances as a function of the angle of attack.

The relationship between down-force and drag is reasonable. You get down-force by flinging air upward and it takes power to fling air around so the drag goes up. Formula I cars trim their wings for a particular course because of this. For a very twisty course that has few straight sections, you want maximum down-force to blast through the corners and the drag doesn't matter so much. On a course that has fewer turns and more straight sections, you want minimum drag so you can go fast on the straight sections and you cool it on the corners. Some cars have so much down-force (>3g) that you could drive them on the ceiling but they also have 700 hp and we can't do this on a bike.

The book has information about the drag of wheels as a function of whether or not they are rotating. We scientists like these goofy experiments even though nobody is going to win the Indy 500 in a car that has non-rotating wheels, so who cares? Whether or not the wheels rotate influences the drag by only 1 or 2 percent, but the lift is affected anywhere from 12 to 43 percent because of the Magnus Effect. This suggests that most of a wheel's drag is due to its translation rather than its rotation. In other words, a non-rotating wheel that sticks out of the top of a streamliner would have about the same drag as the ones that touch the ground and this drag is substantial because a non-disk wheel is aerodynamically lousy.

I am becoming increasingly convinced that the fast bikes are the ones with the good detail work and that a variety of shapes work well. If you leave gaping holes in the side for the handlebars to swing out and you leave the entire bottom open, you will not have a fast bike no matter how long the nose or tail. (Don't ask me for the web site that shows my first streamliner!) Some very fast streamliners have rather blunt noses, but their detail work always looks great. It seems that it's important for the fairing to be one nice blob as opposed to a conglomerated mess of different pieces like a car. You can measure how well the detail work was done by listening to the bike go by. If you can hear much of anything, it wasn't done right. The Varna streamliners, for instance, are very quiet even at high speeds.

The book says this about Kamm-Backs: An aim of shape development is to make the static pressure at the end of the vehicle's body, the so-called base pressure, as high as possible, and the base itself, where this base pressure acts, as small as possible. This requires drawing in (tapering) the rear, a technique called "boat-tailing". Figure 4.43 shows the extent to which the drag of a body of revolution can be reduced by tapering. The optimal tapering angle of 22 degrees given in this diagram should be taken only as indicative; the specific optimal angle depends on the upstream history of the flow. Extending the rear end encounters a saturation effect; with increasing length the positive effect on drag becomes progressively weaker. If the rear end is properly truncated, which is called bob-tailing, very little drag-reduction potential is lost. This confirms the idea of Wunibald Kamm. Kamm's conclusion was that you should find the point where the tail is half as wide as the maximum width of the vehicle and cut it off there. There is little benefit in having it extended beyond this point because the piece that you keep effectively tricks the air into thinking that the rest of it is there anyway.

My overall impression of the book is that it is full of interesting data and it is very informative. If you are interested only in information that is relevant to building a streamlined bike, then much of the book will not be applicable. If, on the other hand, you are a scientist like me, then you will find the whole book fascinating. I doubt that anyone who bought it would be disappointed.

Aerodynamics of Road Vehicles Edition: 4
Editor: Wolf-Heinrich Hucho
Date Published: 1998
It is available from the Society Of Automotive Engineers Bookstore
SAE Member Price: $99.00
List Price: $99.00
ISBN Number: 0-7680-0029-7
Number of Pages: 938
Binding: Hardbound
Order Number: R-177

Table Of Contents:
1. Introduction to Automobile Aerodynamics
2. Some Fundamentals Of Fluid Mechanics
3. Performance of Cars and Light Trucks
4. Aerodynamic Drag of Passenger Cars
5. Directional Stability
6. Function, Safety, and Comfort
7. Wind Noise
8. High-Performance Vehicles
9. Commercial Vehicles
10. Motorcycles
11. Engine Cooling
12. Heating, Ventilation, and Air Conditioning of Passenger Cars
13. Wind Tunnels
14. Measurement and Test Techniques
15. Computational Fluid Dynamics