DESIGN AND CONSTRUCTION  OF A LAND SPEED RECORD   
 STREAMLINER

DESIGN TOPICS

Copyright 2012 and 2013, all rights reserved.
No part of this website may be copied or distributed without the author’s express written permission except for research, personal use, or brief excerpts for quotation.

DISCLAIMER - README:

Notice to everyone who reads and/or makes use of any information on this website. I make no claim, warranty, or assurance that any aspect of the information that you find on this website is correct or complete or useful. If you make any use of it, you do so entirely at your own risk. You agree to this by the act of reading and/or using any information presented on this website. Take all of the information and conclusions presented on this website with a "grain of salt." I accept no liability for any damage or injury that might result from making use of any aspect of this website. If you have any doubt about any aspect, carefully check it out. The responsibility for using it rests entirely with you.

There is a fine line between recklessness and courage.
Paul
McCartney

 
 

  DESIGN TOPICS TABLE OF CONTENTS   Technical discussions of various aspects of streamliner design.
  • INTRODUCTION Updated October 2012
  • SAFETY EQUIPMENT Updated October 2012
  • AERODYNAMICS Now on separate page as of December 2012
  • FRICTION, TRACTION, TIRE SLIP, AND WHEELSPIN Updated April 29, 2013
  • ROLL CAGE STRENGTH, STIFFNESS, AND SAFETY December 2012
  • ROLLING RESISTANCE September 2012
  • WHEELS AND TIRES August 2012
  • CHASSIS Coming soon
  • COOLING Coming soon
  • SUSPENSION April 2013
  • WEIGHT September 2012

 

INTRODUCTION

On this page of the website I document data, analyses, and conclusions regarding burning questions that came up during the project. I refer to it often to refresh my memory during the design and build cycle. I used engineering analysis, equations, tables, and graphs to understand and decide on performance and design aspects. I included mathematical discussion that supports conclusions. I tried to write this page, and the performance page, so that a reader who is so inclined can skip the equations and still come away with the essence of conclusions. The information and calculations are applicable to streamlined cars and motorcycles and to some extent to any type of land speed record vehicle. I went to considerable effort to ensure that the information is correct. I carried out the analyses using formal education plus experience as a registered professional mechanical engineer (P.E.) with advanced degrees. I am a member of SCTA/BNI, USFRA, and AMA. I have studied SCTA, AMA, and FIM competition regulations and successful streamliners. I have raced and tuned motorcycles. I once again stipulate that I make no express or implied guarantee as to the correctness or usefulness of anything in this document. If you make use of it, you do so entirely at your own risk. 
 

Judgment, planning, concentration, caution –all necessary!

Cojones grandes – not so much.

SAFETY EQUIPMENT

LSR sanctioning organizations require a rather extensive array of safety equipment, virtually all of it required to be SFI certified. The home page photo of the mockup shows some of it being worn - helmet, HANS device, and SFI-approved 7-point harness, fire suit, and gloves. Other required apparel includes boots, and Nomex long-handle underwear, socks, and head sock. Arm restraint straps and leg restraint means (I plan to use NASCAR window net) are required to retain body extremities inside the vehicle. Roll cage padding, a fire suppression system, and one or more parachutes are also required, with detailed specifications that depend on class and anticipated speed. I chose a fire suppression system that considerably exceeds the minimum requirements. For my class and speed, one parachute is required, though I expect to possibly achieve the a speed that would require two. I will have three parachutes, to provide backup in case of deployment failure. There regulations also specify chassis construction safety requirements.
 
AERODYNAMICS

This section is now on a separate page and will be substantially expanded.
 

 
FRICTION, TRACTION, TIRE SLIP, AND WHEELSPIN

Friction wastes power in the engine and driveline and so reduces top speed, but without friction there would be no traction. Acceleration, wheel braking, steering, and resisting crosswind and centrifugal forces in a turn all require traction. Traction depends on the horizontal force that can be developed between the road surface and the tire at the contact patch. A simple model that can be very useful in this regard, if used correctly, states that the horizontal friction force that can be developed is less than or equal to the product of the force N perpendicular to the ground (often called the normal force) and the coefficient of friction μ between the tire and the ground. This relation can be written in equation form as

F ≤ N * μ.

Here "≤" means "less than or equal to, but never greater than". The friction force that develops is just equal to the force tending to cause the tire to slide, until the maximum possible value is reached, after which the tire will skid or wheelspin will occur. The normal force N is due to vehicle weight plus additional forces such as “weight transfer” during braking or acceleration, aerodynamic drag and lift forces, and dynamic forces exerted by the suspension and irregularities (bumps) in the track surface when the vehicle is in motion. 

While designing my streamliner, I gradually came to better understand friction and how it affects land speed racing performance and safety. I am still working on it. Confusion and misinformation about friction and tire adhesion abounds. A common elementary friction model states that the value of the coefficient of friction is independent of the contact area. This is a “rigid body” friction model that is of little use in the real world. If correct, wide soft slicks would not give better traction than hard skinny tires. The actual situation involves the strength of the tire and road surface materials, the contact patch area, and molecular cohesion and adhesion. I have seen statements that the static friction coefficient value cannot numerically exceed 1. This is not correct, though it is a reasonably good working estimate for rubber tires on pavement under ideal dry conditions. Specialized tire designs and rubber compounds, elevated tire temperature, special track surfaces, and surface treatments such as are used at drag strips, can yield values considerably higher than 1.


One source of possible confusion is the difference between "wheelspin," and the term "tire slip." By "wheelspin" or "skidding" I mean that there is sliding contact between the entire tire contact patch and the track surface. "Tire slip" and "slip angle" (as I understand them, anyway) measure the fraction of the contact patch that is sticking. Tire slip is quantified by a formula known as the "Pacejka magic formula" developed primarily by the Dutch university professor Hans Pacejka. A curious aspect of this extremely complex subject is that some tire "slip" (not sliding or wheelspin) is necessary for a tire to generate traction, and that there is an optimum amount of tire slip. This does not imply that wheelspin or skidding is desirable in land speed racing or in drag racing.

The numerical value of the coefficient of friction depends on the tire material and the track surface. Being able to estimate the maximum friction force is useful for predicting whether sliding (wheel spin and/or skidding) will occur under various conditions. This is particularly useful for estimating the driving force available to accelerate the vehicle, which is a critical aspect of top speed estimation algorithms. The friction force is also a critical aspect of lateral stability and braking. A working estimate of the friction force is also useful for estimating forces and torques on the frame and suspension components for stress analysis and to estimate stopping distance and the speed at which the brakes should be or should not be applied.

For any given pair of tire and track surface materials, for any given conditions (wet, dry, oily), there are two (not just one!) values of the coefficient of friction μ that are of interest; the "static" or "no-slip" value and the "sliding" or “dynamic” value. The sliding value is always smaller than the static value, which is why spinning the tires, fun though it may be, results in smaller acceleration. Think about "going up in smoke" at the drag strip, or how you must steer into a skid to regain control.
  


 
I measured the coefficients of friction between the Bonneville salt surface and a rubber tire using the apparatus shown in the above photo. It is essentially a wooden platform with rubber tire mounted below and a concrete block on top. The "rubber tire" is actually three sections of a motorcycle tire backed up by wood at the center of each tire section, which limits tire distortion and thus simulates a tire with high inflation pressure. I measured the weight of the apparatus by suspending it on the hook of the spring scale shown in the photo. This weight is the vertical normal force when the apparatus is in the position shown in the photo. With the apparatus in the position shown, I exerted and measured a horizontal force on it by pulling on the spring scale in the horizontal direction. I started by pulling gently and gradually increased the horizontal force. At first the apparatus did not move; the horizontal friction force developed was just sufficient to balance the force I was applying (the “less than or equal to” aspect of friction). Finally, the horizontal force I exerted became equal to the maximum friction force that could occur, which corresponds to the static coefficient of friction, and the apparatus began to slide. Once the apparatus began to slide, the horizontal force required to keep it sliding was less than the force required to first cause it to slide, which corresponds to the sliding coefficient of friction. The coefficient of friction is equal to the horizontal force divided by the normal force, as defined in the formula presented earlier. On that particular day, I measured a static coefficient of friction of about 0.6 and a sliding coefficient of friction of about 0.45 (25% smaller!). The actual values can vary over a large range, depending on environmental conditions, and may approach zero at the low end. The traction, and coefficient of friction, for a wet surface is, as you certainly know, usually much smaller than when the surface is dry.
 
The friction force must provide longitudinal force for braking or acceleration and also lateral force for directional control. A useful concept is the "traction circle" that graphically depicts the possible relative magnitudes of longitudinal (acceleration/braking) force and lateral force. If the vector resultant of all horizontal forces exceeds the maximum available static friction force, the tire will skid or spin relative to the ground, and the available horizontal force is then the smaller sliding friction force. If more of the available friction force (traction) is being used for braking or acceleration, less is available to resist sliding sideways. This is why suddenly applying more throttle in a turn, when centrifugal force is loading the tire sideways, can cause the rear end of a rear-drive vehicle to step out (oversteer). This also means that a tire that is skidding or is in wheelspin can provide less lateral force to maintain directional control. On ice or snow or other slippery surfaces, if you begin skidding, you turn into the skid to get the tire rotating (not slipping on the road) instead of skidding and slipping. A good Wikipedia traction circle article titled "Circle of Forces"may be found at http://en.wikipedia.org/wiki/Traction_Circle.

Wheelspin occurs when torque at the rear wheel is sufficient to break traction. This is most likely to occur when the transmission is in a lower gear and the engine rpm is in the vicinity of the torque peak. The fact that the sliding coefficient of friction is smaller than the “static” (non-sliding) coefficient means that the total available traction force is smaller if the tire is sliding or spinning. Thus wheelspin reduces the force available to accelerate the vehicle. This is the underlying reason why the drag strip practice of spinning the tires on launch was abandoned long ago (a burnout prior to a run is routinely done to raise the tire temperature and thus the coefficient of friction). Wheelspin not only reduces the accelerating force but also abrades the tire and increases tire temperature. Tire survival depends strongly on temperature, as well as inflation pressure, rotational speed, and load, because rubber strength declines as temperature increases. Tires can be shredded and destroyed by excessive wheelspin, which is both expensive and dangerous. In summary, wheelspin reduces available acceleration force and thus the maximum speed that can be reached in a specified distance, reduces directional control capability, and reduces tire survival, thus degrading both safety and performance. It also causes ruts in the track. 
 
 


This photo shows an example of the damage that excessive wheelspin or skidding can do to expensive LSR tires.  
   


Wheelspin can be avoided by a “traction control” system, by careful throttle modulation by the driver, and by shifting up at a lower engine speed (short shifting), but doing these things advantageously is not easy. Traction control and ABS systems try to allow accelerating or braking forces to increase just up to, but not beyond, the point of incipient sliding motion between the tire and the track surface. Some current systems do not do this better than a highly skilled driver, but the principle remains the same. It is just possible that a small degree of wheelspin may be advantageous, since heating of the tires typically increases the coefficient of friction, but this strikes me as a risky procedure. Tire warmers, as used in road racing, may be worthwhile, though I do not know the optimum temperature for land speed tires.


For a vehicle with a smallish engine, such as my streamliner, wheelspin is likely to occur on good salt conditions only in the lower gears and if the engine speed is near the peak of the torque curve. Some vehicles however have sufficient torque to spin the wheels at virtually any speed, making wheelspin difficult to avoid.
   
WEIGHT

This section will be expanded.

I have seen and heard people say that weight doesn't matter in land speed racing.  Is this true? I have done some physics-based investigation of this question, and find that the answer is "it depends." For a 4-wheel-drive vehicle with enough power to spin the wheels at any speed, it may be true that weight and weight distribution do not affect top speed. For vehicles with smaller engines, which have limited torque and power, weight and weight distribtion definitely are important issues. I will refine my analysis of this and post it here.  For now, here are a few thoughts.

It seems to me that land sped racing is rather similar to drag racing on a long track.

In most forms of racing, great effort is expended to minimize weight. Weight (ballast) may be added in a particular location to improve handling, traction, or weight transfer, and to avoid wheelspin, usually while staying just above the legal minimum weight. Additional vehicle weight increases tire loading and always requires more driving force at the ground and/or additional distance to accelerate the additional mass to the same speed. Adding weight to increase the weight bias to the driving wheel(s) may increase or decrease top speed, depending on details of how much of the time the available torque can spin the drive wheels. Careful consideration is warranted before adding vehicle weight, even for valid safety reasons such as added chassis strength. Additional weight can actually degrade safety due to increased tire loading. Adding weight to counteract lift may be required if the body shape and angle of attack produce too much lift and cannot be modified. I endeavored to minimize both lift and vehicle weight, within practical and economic limitations, to the extent possible without compromising safety.
 
ROLLING RESISTANCE

Achievable speed depends on the engine power and the resistance that has to be overcome. The resistance includes driveline losses in the transmission and final drive, aerodynamic drag, and rolling resistance. A mathematical model that describes each of these is required for performance modeling and to understand what measures are possible and worthwhile to maximize top speed. Rolling resistance includes brake drag, friction in the wheel bearings and suspension system, aerodynamic drag (“windage”) of the rotating wheels, and energy dissipation within the tire due to deformation and hysteresis. The amount of energy dissipated in the tire depends on (Bradley 1996) tire construction, the road surface, tire temperature, tire pressure, speed, the contact force between the tire and the road, and the amount of driving force exerted by the tire. The vertical force at the tire contact patch depends on vehicle mass supported by the tire, weight transfer during acceleration, and aerodynamic lift and drag forces. Weight transfer and aerodynamic forces vary continuously with speed and acceleration during a run; both are zero when the vehicle speed is zero.

Improving the efficiency of the driveline components and minimizing brake drag are basic measures to reduce rolling resistance. Using oil rather than grease to lubricate the wheel bearings reduces rolling resistance, provided that the oil temperature can be controlled and oil leakage avoided. High pressure in the tires helps to minimize deformation at the contact patch, but too much pressure can distort a wheel or cause a tire to fail. Measurements have conclusively shown that rolling resistance increases directly with vehicle weight, a good reason to reduce vehicle weight where safety permits.


A coefficient of rolling resistance can be defined as R = FR / W, where FR is the resistance force that opposes motion and W is the weight carried by the tire. Various internet websites give values of the coefficient of rolling friction R ranging from 0.0002 for a steel wheel on a steel rail to 0.3 for a car tire on sand. Values were found that ranged from 0.006 up to 0.015 for car tires on pavement. A single value for R is of limited value to land speed racers; we need to know how R varies with speed and other factors.

Metz (2004) discusses an equation for rolling resistance credited to another reference (Gillespie) that includes an accounting of the variation with speed V in units of mph:

R = FR / W = 0.008 + .0065 (V/100)
2.5

Hucho (1998) presents rolling resistance data as a graph that I least-squares-fitted, using the general form of the above equation, to obtain

R = FR / W = 0.012 + .00324 (V/100)1.76

Hoerner (1958) suggested a more detailed model that includes the effect of inflation pressure as well as speed and tire load. Cossalter (2006) discusses a model based on Hoerner’s suggested approach, which is discussed in more detail by Bradley (1996), who attributes the parameter values to Kevin Cooper. This model was developed to describe rolling resistance of a land speed record motorcycle but is useful for any vehicle. It is presented for two speed ranges, and units are pressure in psi, weight in lbs, and speed in ft/sec. The rolling resistance values calculated from these two equations do not exactly match at the 102 mph boundary speed unless the tire pressure is small, much lower than would be used; at realistic tire pressures, the low speed equation gives large rolling resistance values.

R = FR / W = 0.0085 + 0.255/p + 0.2771 (V/100)2/p         (V < 150 ft/sec = 102 mph)

R = FR / W = 0.255/p + 0.51 (V/100)2/p         (V > 150 ft/sec = 102 mph)

For use in performance prediction analysis, I needed to have a single equation over the entire speed range. I used an initial coefficient of 0.006 and the second term from the Hucho data curve fit, as follows:

R = FR / W = 0.006 + .00324 (V/100)
1.76

This model rather closely matches the Cooper model for high tire inflation pressure at higher speeds.

Values of the rolling resistance coefficient R from the various models are plotted in the accompanying figure, and the resistance force FR = R W for a 1000 lb vehicle in the next figure. The resistance force FR values can be extrapolated to vehicles of a different weight, higher or lower, by multiplying by the weight ratio. At 250 MPH the rolling resistance for a 1000 lb vehicle is shown to amount to about 20 pounds (but possibly much larger according to some of the models). In another section I estimate the aerodynamic drag of my streamlined motorcycle to be on the rough order of 75 pounds at 240 mph. This indicates that rolling resistance plays a secondary but significant role in determining the top speed of a low-drag streamlined vehicle that uses high tire pressure.

These models give very different values for how the rolling resistance increases with speed. This may be due to the effect of tire inflation pressure, as indicated by the Cooper models for various tire inflation pressures. None of these references provide any quantitative information regarding to what extent aerodynamic drag of a rotating tire (sometimes called windage) is included in the models. Cossalter does point out that rotating wheel aerodynamic losses depend on the form of the wheel such as arms or spokes, the profile of the tire, and the rotational speed.



Rolling resistance coefficient models.
 



Rolling resistance for a 1000 lb vehicle.
 
 

WHEELS AND TIRES

Sanctioning body regulations place no limits on streamliner wheel diameter. A small diameter front tire enables the pilot of a two-wheel vehicle to see the course, and facilitates smaller vehicle height and thus frontal area and drag. The rear wheel is required to be the driven wheel of a motorcycle. A larger diameter rear tire allows use of a larger diameter rear chain drive sprocket for a given overall drive ratio, which facilitates use of rear sprockets in available sizes to achieve final drive ratios needed at Bonneville, and also reduces rear wheel rotational speed. Tires are obviously major safety and cost considerations in land speed racing. It would be convenient and cost-effective to use high performance motorcycle wheels and tires, which are typically 17” “W” rated tires rated by the tire manufacturer for 168 mph continuous speed. The W rating is the second highest speed category for commercial tires; the highest is “Y” which is a speed rating of 186 mph. A Z-speed rating only implies that the tires are rated for some unspecified speed that is greater than 149 mph. The outside diameter of these tires is about 24 to 25 inches (0.61 to 0.63 m), which is larger than desired at the front and smaller than desired at the rear.

The SCTA rulebook states that tires with hard compound, with the tread depth reduced by 2/3 (presumably to help avoid tread failure due to stress in the rubber resulting from centrifugal force), can be used up to speeds of 265 mph. Since this is higher than my target top speed of 240 to 250 mph, stock R6 tires and wheels could perhaps be used. A spin test of these tires, indeed any tire that is to be used at such high speeds, is advisable, preferably at a rotational speed higher than the highest expected speed.

Tires rated for a higher speed would provide an additional, highly desirable, safety margin, and allow the vehicle to be used at higher speeds in the future. For speeds higher than 265 MPH, the SCTA rulebook requires LSR (land speed record) or racing tires rated for a speed higher than the class record. Racing tires generally use soft compounds and so would not seem to be the best option, but they may provide better traction.

Goodyear Eagle Land Speed tires are 15-inch tires that are rated by Goodyear for 300 mph speed, and each tire has a load rating greater than my entire vehicle weight. These tires cost about $500 each - expensive, but might seem worth the price at the instant that a lesser tire fails at high speed. I plan to use a 21x5-15 front tire and 28x4.5–15 as the driven rear tire.  Tire information is available at  (http://www.racegoodyear.com/tires/pdf/drag_front_runner.pdf). These Land Speed tires should not be confused with the less-expensive Goodyear “Front Runner” dragster front tires. Goodyear also makes a tire rated for much higher speeds; it is considerably more expensive and has additional use restrictions. Land speed racers also successfully use Mickey Thompson tires that have recently become available.

The Goodyear Land Speed tires are car tires that must be mounted on car wheels to be safely used, since car and motorcycle tires use different bead seat profiles on the wheel rims. One option, which I plan to use, is to design and build custom hubs to mount car wheels. Another option would be to use motorcycle wheels of appropriate size (3.5” or 4” width and 15” diameter in this case) with rims modified to car bead shape. Still another option is to machine custom wheels.

Another tire issue is tread shape. A car tire uses a basically flat tread with rounded shoulders. A motorcycle tire must have a curved tread cross-section to enable the motorcycle to lean in a turn, though only a small lean angle is likely to be required for a streamliner. Other land speed racers have successfully used these tires on motorcycles by using high tire pressure (which also reduces rolling resistance) and mounting the tires on narrow rims to give the tread enough tread cross-section curvature to be useable on a motorcycle at Bonneville.

Another option that has been used successfully by some land speed racers is to make a one-piece wheel and tire of aluminum. This makes for a very durable “tire” that, if properly designed, is not likely to fail. A disadvantage may be less traction on the salt surface, though I have not measured this. A knurled tread surface may help, though this might quickly load up with salt and have no effect.

I chose Centerline brand aluminum racing wheels with a lug bolt pattern known as “VW wide-5,” which is 5x205mm (8.07 inches), made for early (pre-1968, I believe) Volkswagen cars. I will use 14 mm (0.55") grade 9 wheel lugs and 14mm wheel lug nuts; these lug nuts (and the wheels) use a spherical seat with a diameter greater than 1". The wheel center hole is about 6.3” in diameter, which is large enough to fit over the outside diameter of a hub-center front wheel hub or over a motorcycle rear hub sprocket mount ring. These wheels are manufactured for racing and are strong and well-made. They are roll-forged aluminum 2-piece wheels riveted together by a large number of large rivets. They are 15” wheels with a rim width of 3.5”, backspace 2” (2.06” measured), and offset -3/16” (-4 mm), which is half of the 3/8” center web thickness. This wheel is symmetrical about the center plane, which is convenient for a motorcycle. I measured radial and lateral run out to be less than 0.020” (0.5 mm) on the wheels that I plan to use at Bonneville. Run out on another of these wheels that I purchased was somewhat larger at 0.060" (1.5 mm). 


ROLL CAGE STRENGTH, STIFFNESS, AND SAFETY

Coming soon.

 
CHASSIS LOADS AND STRESS

Coming soon.
 

SUSPENSION 

Here are some references that provide useful information.




COOLING and VENTILATION

I have analyzed and compared air cooling and water reservoir cooling. I will refine the analyses and post them here in the near future.

 

Copyright 2012 and 2013, all rights reserved.
No part of this website may be copied or distributed without the author’s express written permission except for research, personal use, or brief excerpts for quotation.

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