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An early step in designing my streamliner was to gather aerodynamics information useful for choosing and refining the streamliner shape. I wrote up what I learned to provide a record that I could consult later (it seems that I do not retain every detail…). Later I rewrote it to hopefully be useful to people whose experience, background, and education may be different from mine. This page, like all pages of my website, is a work in progress. I will date each section when I create or modify it.

My aim in this section is to discuss facts and conclusions that I gleaned during an extensive study of a wide variety of published materials, with emphasis on aerodynamic characteristics of ground vehicles, particularly aspects that contrast with more readily available information about aircraft. My sources are listed on the “References” page. I first present basic concepts that are needed to make effective use of aerodynamic data, especially lift and drag data from sources such as wind tunnel experiments and CFD (computational fluid dynamics) software calculations. I include equations and graphs, and I tried to write so that everyone can take away what they mean.

My overall goal was a body shape that will minimize drag and manage lift forces. Both drag and lift are strongly affected by body shape and size, surface smoothness, and surface irregularities. I chose a very-low-drag plan-view body profile that is based on a NACA 66-010 “laminar airfoil” shape. I will construct the body to be smooth and as free of surface irregularities as I can make it, with the objective of reducing drag and delaying boundary layer transition and/or flow separation. The body shape is intended to minimize lift forces for several reasons. Minimum drag usually occurs when the lift is zero. Upward lift reduces tire contact force, which reduces traction and steering control and may lead to skidding or to the vehicle becoming airborne and crashing. Aerodynamic downforce (downward lift) increases available traction and steering control, but also increases drag and tire loading. Aerodynamic forces vary with the square of speed; effects are small at low speeds, which is where increased traction to avoid wheelspin is most needed.

Basic Concepts, Aerodynamic Coefficients, and Reynolds Number

 Air flow around a vehicle is quite complicated, especially as viewed by a stationary person watching the vehicle pass by. The flow is easier to understand as viewed by a person riding in/on the vehicle or watching the flow in a wind tunnel. Air flow over a body results in changes in air velocity in the immediate vicinity of the body. This causes changes also in air pressure and fluid stress. A basic principle of fluid mechanics and aerodynamics, in fact the central tenant of boundary layer theory, is that a fluid has the same velocity as a body at the body surface, and then changes to match the air velocity at some distance away from the body, usually a fairly small distance. This distance is known as the boundary layer thickness, for which there are a number of definitions and calculation algorithms.

Here is a brief description of air flow over a body. At slow speed, the flow over the body is a smooth flow known as “laminar” that has a rather gradual “velocity profile,” that is, how velocity changes from the body speed at the body surface to the general speed of the surrounding air. This change in velocity takes place in a thin layer on the body known as the boundary layer. Under some circumstances laminar flow can separate from the body, often resulting in a low pressure region that increases drag. As flow speed increases, laminar flow goes through a transition into “turbulent” flow, which is descriptively named; the flow whirls and twirls on a very small scale, the velocity profile change is much steeper near the body surface, and drag is higher compared to laminar flow. Turbulent flow can also separate from the body, though separation is less likely than in laminar flow. Sometimes a flow can separate from the body, become turbulent, then reattach to the body, and perhaps again separate from the body further downstream. Sometimes a flow is purposely made turbulent, if the situation is such that the increased drag of turbulent flow is smaller than the increased drag of separated laminar flow. This is why a golf ball has dimples; reduced drag yields longer flight distance. Tripping the flow from laminar to turbulent is a specialized technique that is not universally useful; it is unlikely that a rough or dimpled surface will reduce your streamliner’s drag. You may have heard that flow transitions from laminar to turbulent flow at a particular value of the Reynolds number (recall the definition of the Reynolds number). This is a useful rule of thumb, but in fact laminar flow can persist to very high speeds, particularly if the body surface is smooth and the air is quiescent. The study of flow transition, known as hydrodynamic stability, is a very complex subject.

Pressure is force per area that acts normal (perpendicular) to the body surface. Fluid stress, due to fluid viscosity, is also a force per area but acts tangent to the body surface. Pressure and friction can be summed up over the entire surface by mathematical integration to obtain resultant aerodynamic forces and moments. It is customary to resolve the forces into a “lift” force that is directed perpendicular to the direction of motion, a “drag” force directed opposite to the motion direction, and a “moment” (torque) that has a magnitude that depends on the chosen reference point in space. Aerodynamic moments can occur about the pitch, yaw, and roll axes.

The magnitudes of lift and drag forces (and also aerodynamic moments) vary with body shape and size and the orientation of the body relative to the flow direction, particularly yaw and pitch (angle of attack). They also depend on flow speed squared (V2) and air density ρ. Dividing lift or drag by the quantity q = ½ ρ V2 (the dynamic pressure) and an area results in a dimensionless coefficient that is approximately constant over a wide range of speed and air properties for a given body shape.  These are useful for comparing shapes because their numerical value is approximately independent of speed, air density, and size. The magnitude of the aerodynamic coefficients depends strongly on angle of attack.

The common aerodynamic coefficients definition equations are listed below.  In these equations, D = drag force, L = lift force, M = an aerodynamic moment, CD = drag coefficient, CL = lift coefficient, CM = moment coefficient, q = ½ ρ V2 = the dynamic pressure or head, ρ = air density, c = the wing chord or body length or other chosen length, and S = an appropriate area as discussed below.

Drag force D is related to the drag coefficient according to

D = CD q S.

Similarly, lift is related to the lift coefficient by

L = CL q S.

The moment coefficient is defined by

M = CM q c S.

These equations clearly show that reducing the area S reduces the aerodynamic force. The reference area S that is used greatly affects the numerical value of the coefficient, so care must be exercised to ascertain the reference area when using or comparing lift or drag coefficient values from various sources. Commonly used reference areas include frontal (cross-section) area, wetted area, and volume2/3 (which has dimensions of area). Wetted area, the surface area per unit span distance, is commonly used for airfoils; it is typically much larger than frontal area, and so results in a much smaller value of the coefficient, which can be misleading when comparing coefficient values. I ran across volume2/3 as the reference “area” in NACA data for airship (blimp or dirigible) bodies. The frontal area is the most commonly used reference area for land vehicles.  At low speeds, aerodynamic lift and drag forces are rather small, but at high speeds they become of primary importance.

Aerodynamicists often express pressure variation over a body or airfoil in terms of a pressure coefficient defined as

CP = (P – P)/q

In this equation P is the static pressure in the fluid at the body surface and Pis the free stream static pressure. The value of the pressure coefficient at the stagnation point is one (which is normally the maximum possible value of the pressure coefficient) since at that point P = P+ q. For speed v less than about 230 mph (Mach number less than about 0.3 at the surface of the earth), compressibility effects are small enough to be ignored. The density is then constant, the flow is then known as incompressible flow, and the pressure coefficient can by written as

CP = (P – P)/q = 1 – (v/V∞)2.

The pressure coefficient is often used to present the variation of pressure or flow speed over a body or an airfoil.

An aerodynamic coefficient’s value is typically not quite constant as speed or size increases. Much of the remaining variation with speed and size can be accounted for by another dimensionless quantity known as the Reynolds number defined as R = V l / ν where l is the vehicle length and ν is the kinematic viscosity of the fluid, which for us is air.  For a vehicle length of 18 feet (5.5 m) and a speed of 240 mph (400 kph) at Bonneville, the Reynolds number is about 35 million (35 x 106). Drag coefficients typically decrease gradually up to a Reynolds number of about 20 million, then remain fairly stable or decline slightly up to about 40 million for both 2-D airfoils (Abbott 1959) and streamlined 3-D bodies (Abbott 1932), and then increase again  gradually with increasing Reynolds number. Thus for my streamliner’s size and expected speed I can use such data to evaluate lift and drag for this vehicle without worrying too much about Reynolds number effects. Reynolds number effects can be very important for extrapolating data from reduced scale models and for very high speeds.

Numerical values of air properties that appear in the equations, which are needed to calculate, for example, drag from a drag coefficient, depend on air temperature and altitude. Typical values at Bonneville in August are temperature of about 105 F, density of about 0.06076 lbm/ft3 (about 80% of the value at sea level) and kinematic viscosity of about 1.8 x 10-4 ft2/sec.


Aerodynamic Coefficient Magnitude

Numerical values of aerodynamic coefficients for a given body shape can guide body shape choice to minimize drag. They also enable physics-based performance modeling to estimate top speed and guide gearing and shift point choice. The numerical magnitude of lift and drag coefficients for a given body come from experimental data and/or theoretical calculations. Engineering tools that are used to quantify aerodynamic forces and moments include wind tunnel testing, coast-down tests, and computational fluid dynamics (CFD). All of these are expensive to do properly, require specialized skill and knowledge, and have limitations for ground vehicles. Detailed wind tunnel data is useful but generally not definitive for several reasons, including that the effects of rotating wheels and of a nearby ground surface moving at the same speed as the air are difficult to simulate in the wind tunnel. Effects of tunnel test section dimensions on the vehicle boundary layer must be accurately accounted for, and the effects of Reynolds number mismatch (Reynolds numbers for wind tunnel data are often much lower than real bodies) must be compensated. Coast-down road testing is difficult to instrument accurately, and aerodynamic drag and rolling resistance effects can be difficult to separate in the data. Flow visualization can help to reveal flow patterns and boundary layer separation in both techniques. Calculated CFD results are useful (if you have the software and adequate computers available and know how to use them, or the funds to commission a study), and are standard tools for aircraft design, but current CFD state-of-the-art cannot yet routinely account for critical details of road vehicles. Top racing teams, especially in F1, and automobile manufacturers, have huge resources to use all three techniques to design their cars. Since I am without budget or time resources to extensively use any of these techniques, I used published and extrapolated data to at least establish trends and guidelines to choose a body shape. 

Some published aerodynamic coefficients data and information for ground vehicles is available, but most of the available aerodynamic data was developed for aircraft. Most aircraft R&D since WWII has been devoted to very high speed jet-powered aircraft with speeds exceeding 400 mph. The majority of the aerodynamic information useful to the designer and builder of a land speed record streamliner dates to the early 1950s and earlier. 

The numerical value of the aerodynamic coefficients for a land vehicle in operation is typically very different form the values obtained from a model suspended in the test section of a wind tunnel. This is because the tunnel test section walls can influence the flow around the body to some extent, and more importantly because wind tunnel data typically does not accurately account for the effect of rotating wheels or the effect of the close proximity of the ground surface on the air flow around the vehicle. For example, it is not unusual for the actual drag coefficient of a vehicle operating on the ground to be twice the value obtained for the same body shape suspended in a wind tunnel test section, and the lift force may be in the opposite direction, i.e. lift rather than downforce or vice-versa.

Center of Pressure

An object acted upon by external forces, if free to do so, will rotate about its center of mass. Important aerodynamic stability considerations for a ground vehicle include the relative locations of the center of pressure, the center of mass (also known as the center of gravity because it is the balance point), and the tire contact patches. The magnitudes of the forces at these locations are of course also of critical importance. Unlike an airplane or boat, a wheeled vehicle may be strongly constrained from rotating in at least some directions by vertical and horizontal forces developed at the tire contact patches. If the vehicle becomes airborne, or if the track surface offers little traction, the effect of the contact patches may suddenly disappear or be lessened. In that case, ground vehicle stability, like aircraft stability, requires that the center of pressure be located behind the center of mass. If the vehicle develops a yaw or pitch angle, the aerodynamic forces acting at the center of pressure will be a restoring force if located behind the center of mass, but will tend to increase the yaw or pitch angle if located ahead of the center of mass, possibly leading to a spin or flip. Thus it is highly desirable to have the center of pressure located behind the center of mass.

Evaluating the effects of aerodynamic forces on a vehicle requires knowing not only their magnitude but also (arguably more importantly) where on the vehicle these forces can be considered to act. The center of pressure of a body is the point at which the resultants of distributed lift and drag can be considered to act as a single force. This is convenient for evaluating the effect of aerodynamic forces on a vehicle (air or ground). The drag force is of course directed opposite to the motion direction. Lift forces are directed perpendicular to the motion direction and are often separately evaluated in the vertical and/or lateral (horizontal) direction. The aerodynamic forces’ magnitudes and locations strongly influence pitch, yaw, and roll stability.

Determining the location of the center of pressure accurately is not easy. The magnitudes and locations of the aerodynamic forces and moments can be rigorously determined by using integral calculus to sum fluid pressure and viscous shear stress forces over the surface of a body. Actually doing this requires not only familiarity with advanced mathematical tools but also detailed knowledge of the variation of pressure and viscous shear stress over the surface of the body, for example via computational fluid dynamics (CFD). The location of the center of pressure can also be determined experimentally in a wind tunnel, but remember that the proximity of the ground surface must be accounted for if the results are to be accurate. I do not have access to all of these required tools and information and so had to find alternate means.

An approximate, much easier, method is to use the area centroid of the projected body profile (Benson, NASA model rocketry website) as an estimate of the location of the center of pressure. This works quite well for long and thin bodies such as a streamliner body or model rocket (but maybe not a roadster or other car) for which the pressure variations over the surface are not large. This can be done mathematically by using area-moments to determine the geometric area centroid. Mathematics can be avoided by finding the balance point of a cardboard cutout of the projected profile, which gives a non-mathematical estimate of the location of the area centroid and thus the center of pressure.

I used the area-moment method to estimate the location of the area centroid, and thus the location of the center of pressure for my streamliner body, including fins and air scoop. The area centroid of the side profile is located at x = 117 inches (x/L = 117/216 = 0.54) at a height of 15 inches above the body keel (46% of the body 32.7” depth). The area centroid of the body top view lies on the body vertical centerline axis at x = 113 inches (x/L = 113/216 = 0.52).

I used mass moments to estimate that the static front/rear weight distribution is about 35/65, with the center of mass located at about x = 110 inches (x/L = 110/216 = 0.51). Thus I estimate that the side view center of pressure is about 7 inches rearward of the center of mass, and 3 inches rearward in the top view, which is favorable for yaw stability. After the streamliner is constructed, I will measure the center of mass location more accurately and adjust it if advisable for dynamic stability. Weight distribution also affects rear wheel maximum driving force and thus top speed.

I am comfortable with the area centroid estimation of the CP for my streamliner, which is behind the center of mass. The vehicle thus will be aerodynamically stable if it loses contact with the surface. I will have dorsal and ventral fins, and also side fins, which will further help keep the front end pointed downrange. NACA wind tunnel data (Hoggard, 1940) indicate that these fins give a substantial restoring yaw moment at yaw angles greater than about 13 degrees. At one point in time I also had a lifting-section vertical tail, which gives a substantial restoring yaw moment even at small angle of attack (yaw angle), up to the stall angle, which is roundabout 13 to 15 degrees. However, this negatively impacts roll stability significantly, and so it was abandoned in favor of a dorsal fin only.

This paragraph discusses a rather esoteric and perplexing (at least to me!) aspect of estimating the center of pressure location. If someone reads this, knows the explanation, and is so inclined, please contact me with the explanation. My streamliner, along with many others, has a top view shape that resembles a symmetrical airfoil. According to aerodynamic textbooks, the center of pressure for a symmetrical airfoil is located at about x/L = 0.25. The center of pressure of a body in motion is defined as the point at which the resultants of distributed drag and lift can be represented by a resultant force with zero resultant moment. The aerodynamic center of an airfoil section is defined as the point at which the section pitching moment does not change with angle of attack up to the point of maximum lift.  For symmetrical subsonic airfoils, the pitching moment coefficient is zero at the aerodynamic center. Thus the aerodynamic center and center of pressure must be at the same location for such airfoils. Aerodynamic textbooks state, and copious wind tunnel data (e.g. Abbott 1959) confirms, that the aerodynamic center of subsonic airfoils is located at about 25% of the chord length. The center of pressure for lift of symmetrical subsonic airfoil sections must therefore also be located at about the 25% chord point, and is independent of angle of attack or magnitude of lift up to the stall angle of attack (typically roundabout 13 to 15 degrees). However, the location of the area centroid of a typical symmetrical airfoil cross-section is located on the mean line at about 40 to 50 % chord. This is the paradox – how can the area centroid be the center of pressure? They are clearly at drastically different locations for a symmetrical airfoil. I conclude that the area centroid does not approximate the location of transverse force accurately for an airfoil section. The center of pressure for a wing must be very different from that of a slender three-dimensional body. So, what does this mean for my streamliner? I had been thinking that, since the top view shape resembles an airfoil, the 25% length CP location might apply. However, the frontal view is oval, nearly circular, so the body is not an airfoil section, not even one of very short span. The body is basically a slender body with fins, like an arrow or a missile, for which the area centroid method is reportedly a quite good approximation of the CP location profile (Benson, NASA model rocketry website).



The obvious objective in designing a land speed record vehicle is to minimize the drag force that impedes vehicle speed. To arrive at an optimized design for a streamlined vehicle, it is useful to be able to evaluate and minimize size (particularly frontal area, but also surface area) and the value of the aerodynamic drag coefficient. Frontal area is often dictated by the shape and size of the driver and engine. Smaller frontal area does not necessarily mean smaller drag force. Body shape affects the drag coefficient, and wetted (surface) area affects the magnitude of fluid skin friction drag. A smaller frontal area combined with a longer length and thus possibly a larger wetted area may or may not decrease the drag force. We must also be concerned with lift forces and aerodynamic moments that can cause loss of vehicle stability. A useful body shape characteristic is the aspect ratio, which is defined as the ratio of length to maximum width. Another parameter known as the thickness ratio is the inverse of the aspect ratio. 

Reported drag coefficients for modern automobiles are generally in the range of 0.2 to 0.6 based on maximum cross-section area, which is also called frontal area. Values lower than 0.2, but realistically not lower than about 0.12, have been achieved for highly streamlined cars. The drag coefficient for racing cars such as Formula 1 cars is much higher, roundabout 0.9; the desire for low drag to maximize top speed is balanced against the need for downforce for braking and cornering to minimize lap time. Downforce is achieved by means of inverted wings and underbody diffusers, both of which increase drag.

For motorcycles, frontal area is problematic to define, so “drag area AD” is sometimes used, which is equivalent to the product of S and CD, or D/q, in the drag coefficient defining equation. Available actual data is scarce. Horner (1958) and Hucho (1998) present approximate order-of-magnitude drag data for motorcycles in terms of AD as follows: AD = 6 ft2 for an upright rider on a non-streamlined motorcycle and AD = 1.5 ft2 for the streamlined NSU 500cc motorcycle that achieved a speed of 180 mph (290 kph) in 1951. The frontal area of this motorcycle was probably about 9 sq ft, indicating a drag coefficient of about 0.17. Modern 1000 cc partially-streamlined superbikes develop about 160 HP or more and can reach a top speed of about 180 mph, and 600 cc bikes develop about 100 HP and can reach 150 mph. I estimate, based on performance calculations using these values, that a partially streamlined motorcycle would have a drag area AD ≈ 4.5 ft2 with the rider bent low. A fully-streamlined motorcycle might attain a value of AD as low as 0.5 ft2 (assuming a drag coefficient of 0.15 and a frontal area of 3.3 square feet, i.e. 2-foot diameter circular cross-section).

Drag force can be calculated using the drag coefficient equation if the values of the other parameters are known. At the altitude and typical August air temperature at the Bonneville Salt Flats, air density is about 0.06076 lbm/ft3 (about 80% of the value at sea level). If velocity is specified in mph and area in ft2, the equation for drag becomes

D = 0.002 CD S V2

Using this equation and the drag coefficient and these drag area values, at a speed of 200 mph the expected aerodynamic drag force for a sport bike (AD ≈ 4.5 ft2 ) is about 360 pounds, and about 40 pounds for a well-streamlined vehicle (AD = 0.5 ft2). The power required to overcome the aerodynamic drag can be calculated according to

P (HP) = 0.00267 * D * V

with D specified in lbs and V in mph. A conventional naked frame motorcycle (AD = 6 ft2) at 200 mph would experience a drag force of about 480 lbs, and would need over 250 HP and a strong, courageous rider to overcome the drag force.

Data presented in Hoerner (1958), Abbott (1932, 1934), and Hucho (1998) indicate drag coefficients of 3-D aircraft and airship bodies to be in the range of about 0.03 to 0.07 based on frontal area (I converted the data presented by Hoerner and Abbott from values based on wetted area and volume2/3 respectively) for a streamlined body of revolution at zero angle of attack, in a Reynolds number range of 10 to 20 million, and located far from a solid boundary such as the ground surface. These references do not provide aerodynamic coefficient values that can be used directly to choose a minimum drag body shape, but they do contain 3-D body data that establish trends that guide the choice of a body profile.

An important design parameter is the aspect ratio, defined as the length divided by the width or diameter. A larger aspect ratio enables a more gradually changing shape that may help to reduce pressure drag, maintain laminar flow, and avoid boundary layer separation, all of which reduce drag, but the increased surface area causes increased viscous drag. These two opposing trends make it reasonable to expect that there may be an aspect ratio for which drag is minimized. After converting published drag coefficient data for streamlined 3-D bodies far from the ground (summarized in Hoerner, 1965) to frontal area basis, a drag coefficient minimum of about 0.03 is found for aspect ratio of about 5 at R = 30 x 106; CD increases to about 0.05 for l / d = 2 and to about .07 for l / d = 8. These data thus clearly show a drag coefficient minimum at l / d = 5 for a body far from a surface. Hoerner also presents data for aircraft fuselages that shows minimum drag for aspect ratio of about 6. Abbott (1932), in a report of a study that investigated air ship body shapes, presents data that also shows a drag coefficient minimum of about 0.05 at about l / d = 5, but with smaller increases for smaller and larger aspect ratios. Abbott also shows that minimum drag occurs at zero angle of attack, and that adding an array of rather large fins to an airship can increase the drag coefficient by 15 to 20%.

Practical considerations, such as minimizing frontal area and weight while yet providing length sufficient to accommodate wheels, engine, and driver, and also stability considerations, lead to aspect ratios that typically are larger than 5 for land speed record streamliners. A motorcycle streamliner is typically a little less than 2 feet wide and a little more than 2 feet high to accommodate the wheels, rider, and engine; length and shape are then chosen to accommodate the wheels, engine(s), driver’s body, parachutes, and other necessary articles, and to minimize drag and manage lift and moments for stability. The length and thus the aspect ratio can be reduced by a more upright driver position, at the expense of increased height and frontal area. A typical motorcycle streamliner will probably have an aspect ratio of about 6 to 10, while car streamliners will be somewhat wider and thus have a lower aspect ratio and larger frontal area.

The presence of the ground profoundly changes the flow around a streamlined body compared to what would occur for a body such as an aircraft that is operating far away from a solid surface. Hucho (1998, p. 20 & 35) presents data that indicates that the drag of a body located near a surface (such as the ground) is higher, by as much as a factor of 2, compared to the drag of the same body located far from the ground. The drag coefficient is equal to the aircraft value if the ground clearance is about 2 times the vehicle height (i.e. about 5 feet or 1.5 meters), and increases as the body is brought closer to the ground, until finally at a small ground clearance typical of cars the drag coefficient is nearly doubled.

An interesting, but speculative and unverified, hypothesis is founded on the idea that flow around a body near the ground is similar to the flow around and between a pair of bodies, the original body and a “virtual body” that is a mirror image reflected in the ground surface, with the pair of bodies located far from the ground. The plane of symmetry between the two bodies is functionally similar to the ground surface, since there is no flow across this plane. The analogy is weakened by the fact that the boundary layer on the ground is not represented. If the bodies are flat-bottom half-bodies, the pair becomes a single streamlined body as they are brought together, with a body thickness double that of the original body, and thus an aspect ratio half that of the original body. If the joined body has an aspect ratio of 5, i.e. near optimum for minimum drag, each half-body has an aspect ratio of 10. This implies that the optimum aspect ratio for minimum drag of a streamlined ground vehicle body operating near the ground may be larger than 5, perhaps as large as 10, more likely some intermediate value. This hypothesis is intriguing but of very uncertain validity. It implies that the optimum aspect ratio may not be very different from the aspect ratio forced by practical considerations. On the other hand, wishful thinking is the enemy of the design engineer.

Choosing My Streamliner Body Shape

Airfoil 2-D data is much more plentiful than 3-D body data and can perhaps be of use to help choose a body shape. Airfoil drag and lift data are available in Loftin (1948) and the classic collection of airfoil data published by Abbot and Von Doenhoff (1959) for many airfoils, and also many other publications, many of which are listed on the References page if this website.

There exists a somewhat obscure type of airfoil known as laminar flow airfoils, for which the profile is chosen to maintain lower-drag laminar flow over as much of the airfoil as possible. These airfoils offer substantially reduced drag compared to most airfoil profiles, at least in some Reynolds number range. The lower drag occurs only for very small angle of attack, about one or two degrees either side of zero. The dip in the drag vs. angle of attack graph is called the “laminar bucket”. At other angles of attack the drag is roughly equal to that of conventional airfoils of similar thickness. The sudden change in drag limits their utility as aircraft airfoils, but seems potentially useful as a streamliner body shape since ideally the angle of attack is always near zero, at least if crosswind is small. This is true even at quite high Reynolds numbers, provided that care is taken to avoid or delay flow separation or transition from laminar to turbulent flow over the body.

Low drag laminar airfoil profiles have the maximum thickness location moved back from the typical 30% of the chord to about 45% to 60% of the chord, which is well-suited to a rear-engine streamliner. Locating the maximum thickness further rearward maintains a favorable pressure gradient (flow velocity continually increasing and pressure continually decreasing), which delays both flow separation and flow transition from laminar to turbulent. This is important because turbulent flow drag is larger than laminar flow drag and flow separation generally results in low pressure regions that increase drag and can negatively affect stability. Flow transition from laminar to turbulent can occur at Reynolds numbers as low as 106 or lower, but hydrodynamic stability research has shown that transition occurs at much higher values if the surface is smooth and the free stream turbulence is low. Such airfoil shapes, converted into a three-dimensional body by rotating the profile about the centerline, may offer reduced drag, though this cannot be concluded with confidence without wind tunnel, CFD, and/or coast-down data. Hoerner (1965, p. 6-18) states that the favorable pressure gradient obtainable for three-dimensional bodies is smaller than for 2-D airfoils.

Example laminar airfoil shapes are (for 10% thickness ratios) are the NACA 0010-35 and 66-010. They have drag coefficients at zero angle of attack that are nearly 50% smaller than conventional airfoils of similar thickness ratio. The available data extend over a range of Reynolds number values from 3 x 106 to 9 x 106. It is likely, though not certain, that this trend would continue up to my expected maximum operating point of 35 x 106. The very low values of drag coefficient occur only at small angles of attack; the low drag jumps to more typical values at angles of attack of more than 1 or 2 degrees in either direction from zero. The effective angle of attack of a 3 mph crosswind (an accepted operating limit for a streamliner) at a speed of 240 mph is 0.7 degrees, which is within the “laminar bucket.”

The 66-0xx airfoil family has a reverse curvature surface which reduces useable internal volume. Loftin (NACA TR-903) reports that the NACA 6-series air foils, all of which have a reverse curvature cusp near the trailing edge, can be modified by replacing the ordinate shape with a straight line from approximately the 80% chord to the trailing edge; these airfoils are designated as the 6A-series. He presents data that shows that this modification does not increase drag for 63, 64, and 65 series airfoils. Unfortunately no data were presented for the 66-series laminar flow airfoil of most interest to me, so this modification would not be guided by data for the 66-0xx airfoil, though it is likely that the trend for tested shapes would continue for 66-series airfoils. Aerodynamic coefficient data are available for the 66-oxx family for thickness rations from 6% to 18%. These data, which I converted from wetted area to frontal area basis, show that the drag coefficient decreases with increasing thickness ratio (decreasing aspect ratio), by about 30% from 9% to 15% thickness ratio (11.1 to 6.7 aspect ratio), which is consistent with the 3-D data discussed earlier that showed a drag coefficient minimum at aspect ratio of about 5.

In the absence of definitive data for 3-D profile shapes of vehicle bodies moving near to the ground, and without the means to refine available drag data, I have tentatively chosen a the NACA 66A-010 low-drag laminar airfoil shape as the leading candidate for the plan view body shape of my streamliner, with an aspect ratio of about 10.

Another possible shape for a streamliner plan view has a constant width central section, with a tapered and/or rounded front and rear portion. This shape may have a stability issue. If a vehicle becomes yawed, for example due to a crosswind, the flow may stall and separate on the downwind side of the body. The separated region will be a low pressure region, which would cause a destabilizing moment about both the yaw and roll axes. For a body that has a constant width central portion and a sharply tapered or rounded nose, the separation can be expected to be located further forward. I am unsure about the likelihood of such a scenario. I chose to avoid the possibility by using a shape that gradually increases in width to about mid-length and then tapers, with no constant-width central portion. A laminar airfoil type shape, with continually increasing width back to about the half-length location, should move the yaw separation location further rearward, reducing the destabilizing yaw moment. The gradually increasing width results in an accelerating flow that tends to resist separation. A laminar flow airfoil shape meets this objective.

Effect of Body Surface Characteristics on Drag

Roughness and surface irregularities can have a large effect on drag (Abbott 1932, 1934, 1959, Hood 1938 {3 reports}, 1939, Loftin 1948, Hoerner 1958). They report that surface waviness can cause premature transition to turbulent boundary layer flow, which results in increased drag. A straight edge should rock smoothly over the surface without jarring or clicking. Objects protruding from the surface can also cause boundary layer transition. Roughness on the order of 0.011” near the leading edge of an airfoil or the nose of a body can cause large increases in the drag coefficient, increasing by a factor of 1.7 to 3. Interestingly, the drag coefficients of both ultra-low-drag and higher-drag airfoils approach similar values when the surface is roughened, though drag coefficients of laminar flow shapes remain slightly lower. For example, surface roughness increases the drag coefficient (based on surface area) of a NACA 0010 airfoil from about 0.0041 to about 0.0093, while a low-drag airfoil such as 0010-35 or 66-010 changes from about 0.0032 to about 0.0090. Small changes in roughness, for which the surface remains relatively smooth, on the order of a finish produced by 320 to 400 grit sandpaper, have little effect on drag. Drag can be substantially increased by surface damage, dirt, rivet heads, insects, scratches, or even camouflage paint and dust that collects on fingerprint oil. Hood presents data that shows that surface irregularities such as rivets, spot welds, panel lap joints, waviness, and roughness, increase the drag coefficient by 5 to 30 percent, especially if the irregularities occur on the forward portion of the profile. Clearly gaps between body panels would thus likely increase drag, especially if they are oriented cross-wise to the flow direction. The drag increases are not additive; for example, while rivets and mild roughness might both cause a drag increase of 30%, the two together result in an increase of considerably less than 60%.

In summary, surface roughness and other smoothness defects such as rivets and panel gaps, along with flow separation, duct inlets, flow through internal passages for cooling and engine induction air, effects of the close proximity of the ground, underbody shape, and flow around rotating wheels, add up to significant additional drag increases. The resultant land vehicle drag coefficient can easily increase from an aircraft value of less than 0.07 to more than 0.15. I conclude that the streamliner surface must be aerodynamically smooth (but it need not be optically smooth), especially near the front, during construction and operation. Assuming a drag coefficient value of about 0.15 seems a reasonable approximation, and possibly an achievable target, for a well-designed and carefully constructed and maintained streamlined motorcycle or car. Based on extensive reading that I have done on the subject, it is about the best that large automobile company research departments have been able to achieve when designing car shapes with the specific goal of minimizing drag.

Drag Calculations

The magnitude of aerodynamic drag as a function of speed can be calculated using the equation for drag force, at least to the accuracy that the frontal area (easy) and drag coefficient (not so easy) are known.

D = CD S ½ ρ V2

CD = the drag coefficient
S = vehicle frontal area
ρ = air density
V = vehicle speed.

The drag coefficient CD and the vehicle frontal area S can be (and often is, particularly for motorcycles) combined into a single parameter called the “drag area” AD = CD S. The power required to overcome aerodynamic drag at any speed is the product of drag force and speed. Note that both the drag force and the power required to overcome drag depend only on speed and vehicle drag area, which depends on shape and size. Aerodynamic drag does not depend on vehicle weight or engine power. Values of the drag force and the power required to overcome aerodynamic drag (not including rolling resistance) as a function of speed V are presented in nearby tables and graphs for selected values of the drag area.  The drag force, for the units shown in the table and graph, is calculated using D (lb) = 0.00203 AD V2, and required power (HP) = 0.00267 D V. Air properties typical of Bonneville in August are temperature of about 105 F and air density of about 0.06076 lbm/ft3.

To be augmented.



 Dynamic and Aerodynamic Stability  

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