One of the big car-geek events that has been on my bucket list is Speed Week, held every August at the Bonneville Salt Flats in Utah. The same place where Gary Gabelich set a record speed of 622.407 mph on October 23, 1970, is also the site of an annual event where anyone can bring pretty much anything they want to and drive it as fast as they possibly can. There are, of course, safety-related rules must be followed, but otherwise it is a run-what-you-brung type of event. The whole thing is organized and run by the Southern California Timing Association (SCTA) and each year attracts around 500-550 cars and motorcycles of every description imaginable. There are production based sedans, pickup trucks, production motorcycles, custom bikes, streamlined bikes, bikes with sidecars, antique roadster-based cars, tank cars (sometimes called Lakesters), and the stars of the show: full custom streamliners. You see a bit of everything on the Salt Flats, but what you rarely see is carbon fiber — a material found in almost all of the fastest cars these days. Here’s why.
No Signs of Carbon Fiber
While spending the week walking around the pits and looking at all the different cars and the way they were built, I noticed something odd. Race cars, especially the ones playing at the top of their field, are usually showcases of many innovative and new technologies. Look at any recent Formula 1 or Indy car and you will see copious use of carbon fiber, Kevlar and other high tech materials in an effort to keep weight down and make the car as fast as possible. Looking at these land speed record (LSR) cars, I saw none of that. The only concession I saw to light weight were aluminum body panels, hand beaten over a streamliner’s frame. Why? Is light weight really not critical to these cars? The streamliner with the aluminum body panels still weighs over 5000 lbs; that’s quite beefy!
Do You Need It?
The more I thought about it, the more I began to wonder if light weight might actually be a detriment to high speed runs. Remember, Formula 1 cars have to accelerate and brake quickly and corner at high G levels. Land Speed Record (LSR) cars don’t have to do any of that — they drive in a straight line and have several miles to get up to speed and several more miles to come to a stop at the end. Formula 1 cars also drive on nicely paved tracks with lots of grip. LSR cars run on salt, which although it seems to stick to absolutely everything, doesn’t provide much grip for tires.
Aerodynamics
https://www.instagram.com/p/CwfwFWIsKaS/
The other factor that comes into play with LSR cars is their extreme high speeds and their aero implications. At 300-400 mph, aerodynamic drag becomes the dominant factor determining how much faster you can go. It takes a lot of force to push a car through the air at those speeds, and all that force has to come from the tires pushing the car forward.
At some point, the force of the drag trying to slow the car down will equal the force the tires can provide to push the car forward. When you reach that point, you cannot go any faster, no matter how more power your engine might have. All that extra power would just cause the tires to spin but wouldn’t make the car go any faster. At that point, what you want is more tractive force from the tires, and since you cannot make the salt any stickier, the only thing you can do is push down harder on the tires to get more friction between the tires and the salt.
You could do this by adding wings, like a Formula 1 car does, but wings add drag. The best and easiest way to increase the friction between the tires and the salt is to make the car heavier. Since we have plenty of acceleration space, the extra weight probably won’t slow us down. In fact, if we have enough power in our engine, the extra traction the weight gives us will help us accelerate quicker and counteract the impact of the added weight. There are limits, of course. We don’t have infinite space to accelerate, and even though our acceleration space is measured in miles, when you’re trying to get up to 400+ mph, those miles get very short very quickly. It becomes a delicate balance between weight, engine power, and aerodynamics.
The Model
To look at this in more detail, I built an Excel model of a LSR car so I could change various parameters and see what their effect would be. The equations are pretty straightforward; the most complicated one is for calculating aerodynamic drag:
Drag = 1/2 x rho x V² x Cd x A
Where:
rho = the density of the air
V = the vehicle velocity
Cd = Coefficient of drag as measured in a wind tunnel or calculated using CFD software
A = frontal area of the vehicle, i.e. the area of the vehicle when seen from the front.
Other things we need to take into account are the friction coefficient between the tires and salt, the weight of the car, the weight distribution between the front and rear axles, the diameter of the tires as well as the tire rolling diameter (SLR), and the tire rolling resistance. If we later want to figure out how much engine power we will need then we also need to know the axle final drive ratio as well as the gear ratios in the transmission. Here are all the inputs we need for our model along with some initial values for a streamliner running at Bonneville (7,000 ft elevation):
With these values, we can start calculating things like the aerodynamic drag as well as the tire drive force. For the vehicle shown above, these numbers are:
As you can see, for a vehicle that weighs 5,000 lbs with a drag coefficient = 0.15 and frontal area = 0.72 square meters, which is quite possible for a streamliner, the drag at 400 mph would be 1588 N while the tire tractive force would be 4445 N. Clearly, the tractive force is more than enough to propel this vehicle up to 400 mph and above as long as we have enough room to get up to that speed.
Next, we can calculate how long it would take for this vehicle to get up to 400 mph and how far it would need to travel to get there, assuming we have enough engine power to keep the tires at their limits of grip at all times. This becomes a little more difficult to do since aerodynamic drag increases as speed increases. Since the force available to accelerate the car is equal to the force provided by the tires minus the aerodynamic drag force, the total acceleration force slowly decreases as speed increases:
From this graph you can easily see that if we were able to continue increasing speed, at some point, the available acceleration force would drop all the way to zero. This is the point where the aerodynamic drag is equal to the tire tractive force and no further acceleration is possible. We will have reached our terminal velocity. With this data, we can now calculate how far the vehicle has to travel in order to get up to speed:
It takes more than 6 miles for our car to get to 400 mph. If we had the salt flats all to ourselves, this might be acceptable, but for Speed Week, this is way too far. The tracks the SCTA normally lays out on the salt are 9 miles long: 1 mile for acceleration followed by 4 timed miles and finally 4 miles to stop. Speed is measured as an average over each of the four timed miles and the speed that is recorded is the fastest of those four readings. So, in reality, you have 4 miles to accelerate followed by the last timed mile.
Given this track payout, if we want our car to go 400 mph at speed week, we need to get up the speed within 4 miles. Clearly, our car will not get there. From the graph, at mile 4, we are only going about 330 mph and at mile 5 miles we are going about 360 mph, so our average over the last timed mile would only be 345 mph.
So, how do we get our car to accelerate quicker? We need more traction from our tires. We could try making our car heavier to give the tires more traction. Let’s make our car 1,000 lbs. heavier:
Now, the tractive force will be:
Tractive force has increased from 4445 N to 5334 N. Aerodynamic drag is still the same so we should have more acceleration force available now. Unfortunately, we also have a heavier car to accelerate and the result is no better performance:
We still need over 6 miles to get up to 400 mph. There is a very slight improvement, but this is because the drag force is a smaller percentage of the available tractive force, not because we’ve made a significantly better vehicle.
We need a way to increase the tire tractive force without making the car heavier, and the way to do this is to shift the weight around, so we have more of the vehicle weight sitting on the drive wheels. Assuming we have a rear-wheel-drive vehicle, we need to move some weight rearward in the car. Let’s assume we can move a bunch of heavy stuff to the rear and increase our rear weight distribution from 50% to 60%. We’ll also drop our weight back down to 5000 lbs since the weight increase didn’t work:
Now, our acceleration results become:
We’re still not quite there. It’s still taking 5 miles to get up to 400 mph, but you can see how playing with these inputs can shift the results and how the overall weight and weight distribution can have a significant impact on our performance.
Now, let’s look at a more common example. Most of the cars at Speed Week are based on common production cars. These cars have a much higher coefficient of drag and much larger frontal area. They also start out lighter than our streamliner.
Of course, we aren’t going to go 400 mph in one of these, but is it possible to go 200? Let’s find out. Here are the inputs for our new car:
Here are the drag and tire force results at 200 mph:
Obviously, the drag force is far greater than the tire tractive force which tells us we can’t get there. If we look at the acceleration graph, we see the same thing:
We can’t get to 200 mph, but we can quite easily get to 160 mph before we start to lose traction. That tells us there’s hope. We just need more tractive force. What would happen if we made our car a lot heavier? Let’s add 2000 lbs:
Here are the drag and traction results:
Our tractive force is now greater than the drag so we should in theory be OK, but do we have enough space to get up to speed?
Yes, we do! We can even go a bit faster than 200 mph. In fact, by the time we get to mile 4, we will be going over 220 mph! And all we did was make our car heavier. We did nothing else. Two thousand pounds is a lot of weight to add, and we wouldn’t need all of it if all we wanted was to just break 200 mph, but you get the point. More importantly, adding that much weight means adding a lot of ballast, and we can decide where that ballast goes. If we put most of that weight towards the rear of the car, then at the same time that we are adding weight, we could also increase the rear axle weight distribution and get even better performance.
Each of these models assumes we are talking about wheel-driven cars and that we have an engine that has the horsepower needed to keep the tires at the limits of traction or else all bets are off. If we don’t have the power, then we certainly won’t get the speed. But what these models do tell us is that saving weight in LSR cars by using exotic materials is actually counterproductive. The only time it might make sense is if the only way to get the speed you want is to change the weight distribution. Then, using lightweight materials might let you add ballast in places that give you the weight distribution you want. If you don’t have that problem, go ahead and make your LSR car heavy. It could actually make you faster!
One last point. Because of the tire traction limitations we’ve been discussing here, there is a limit to how fast wheel driven cars can go. So far, the record for a wheel driven car is 503 mph set by the 4,950 pound pound Team Vesco Turbinator II on October 1, 2018 at Bonneville. If you want to go significantly faster, you have to move up to a rocket powered car in which case the tire question becomes moot. Your top speed now just depends on the power of your rocket motor.
So in this case does a racing slick cost speed because less traction and a mudder tire help because more traction? In truck sled haulers big fanned tractor tires help traction to pull the sled. In some cases farmers fill tires with water or sand for weight has this been tried?
I don’t know but whatever you put in there can’t shift around or the balance would get screwed up and be different every time.
Basically weight stays on the end. They do not fill the tire completely. But good point
In the 1970s farmers in California would fill their tractor tires with water for extra traction without putting stress loads on the tractor. If farmers were doing this elsewhere I imagine that antifreeze was used There was even a company that filled (and unfilled tires with powdered lead. Obviously a bad idea.
Calcium Chloride solution.
Not as common any more, but still done on smaller tractors. Bigger tractors are trying to lessen their compression footprint, not increase it.
Now that I think of it, this was for subsoiling. The neighbors would do this, we just used a caterpillar that we welded extra deep treads on and a 55 gallon export oil barrel filled with concrete hung off the front.
We can compare the body work a bit to a wing of an aircraft. Often the delta in weight is not a massive percentage. Important on a heavy assy like a large wing that can justify the additional cost. But a few percent off 5000lbs isn’t much.
Not to mention the skin on a carbon wing can get real thick. I worked on a program where large sections of the wing were 5/8″ thick carbon fiber.
Machined frames with a stretched skin pulled over them is easy and cheap compared to the tooling to create molds for CFRP.
Huibert, good analysis! Though it looks like you’ve left rolling resistance from your equation of overall drag force.
The full set of equations used to calculate total drag (FD) on a car from all sources is called the proving ground equations: FD = AR + RR + GR, where AR = aerodynamic resistance, 0.5*rho*Cd*A*v^2 as you’ve calculated, RR = rolling resistance = Crr (coefficient of rolling resistance)*Fn (force normal to the ground – normally vehicle weight but this can change with aerodynamic lift or downforce), and GR = grade resistance, which is zero for a perfectly flat surface like Bonneville.
Rolling resistance is usually modelled as a constant given a fixed tire/road combination, but in reality it is more complicated than that, and I’ll bet all sorts of interesting things start happening on the salt flats. In reality the rolling resistance of tires starts to increase with increasing speed, normally right around 60 mph or so for passenger car radials. Evidently bias ply tires were worse for this phenomenon. The way it has been described to me is that a standing wave gets set up in the tire, and at a certain speed the vehicle starts to ‘outrun’ that standing wave and starts climbing up it… I’m not sure if that is a really valid model for what is happening, since it sort of implies you could get ‘over the hump’ of increased Crr if you powered through that speed range, but I don’t think that is actually true. Unfortunately tire rolling resistance performance is some of the least publicly available automobile performance metrics there are, especially outside of normal road speeds.
I also seem to recall that the actual fit of aero drag to empirical data isn’t quite V^2 but to an exponent slightly higher than 2, which starts to matter quite a bit at high speeds, though now that I go to look for published info to back up that statement I can’t seem to lay my hands on it.
One thing I’m certain of, though, is that 380 hp isn’t going to get anything to 400 mph, wheel driven. Nolan White (RIP) is one of the slowest members of the 400 mph club, and his streamliner took two small block Chevy’s with blowers on them to get him to 422 mph. Goldenrod ran 4 Hemi’s for a combined 2400 hp. Keep in mind there are only sixteen members of the 400 mph club so far.
Actually, I didn’t. The tire rolling resistance is buried in the other equations. The drag equation was only to show aero drag. For lack of knowing any better, I assumed a 6 kg/ton rolling resistance for each tire since these tires are special high pressure LSR tires.
Aha, I see it there now. I suspect Crr of less than 1% is probably optimistic considering the loose surface, but as I mentioned before, that’s speculation – there is just so little published data on rolling resistance, especially as it varies with speed, inflation pressure, etc.
I suspect the wheel driven cars getting up to 400+ mph are spinning all four tires, all the time. The power vs. tractive effort may be more akin to a speed boat than what we normally think of as a car. And that’s a sobering enough thought to keep me off the salt, thanks very much…
Also, carbon fiber is extremely expensive to produce in minimal, maybe one of one situation. And has a tendency to not deal with unexpected forces well. I imagine in a situation where you’re going a couple hundred mph, that could be challenging and costly to both design and produce. Plus the risk of catastrophic failure at 450 mph, probably puts people off.
Even in drifting, which I know better than LSR. Anything not off the shelf is way to expensive and failure prone. There’s a clear benefit for its usage when possible. But even F1 teams have budgets now.
I’ve made one-off carbon parts, including some for my British Drift Championship MX5, like the front fenders to clear the front wheels with extra steering lock. If you mould the parts yourself, and worry more about function than looks, you can make some useful parts for not much money and only moderate effort. The front fenders were done in a weekend, including the second skin of internal stiffening. That’s the benefit of having OEM parts to mould over.
They lasted pretty well, they both got cracked in crashes, but I fixed them with cable tie stitches, because drift car.
I, and most people over here run fiberglass. When you buy in bulk it can get pretty cheap, like sub-100 for full fenders or a wide body that is basically the fender. A mould at home, set up works for fenders, but not alot of benefits over fiberglass.
Really the benefit in drifting is the ability to run pretty extreme shapes without adding weight in carbon aero packages. For most people it wouldn’t matter. But, this and last year, we’ve seen a lot of high horsepower cars even in grassroots that just can’t grip. All these supercharged and nitrous v8’s with their instant tongue. Being able to add some downforce while minimizing you acceleration loses would be hella helpful. That’s a significant R&D and development cost though, that maybe only RTR, Forsberg and Turck could swing. Notable they are the only people who are factory backed.
Fascinating! I love counter-intuitives.
I have a similar spreadsheet where I look at aerodynamic drag vs speed, and then with speed vs time/distance data from my OBD2 reader & GPS, I can back-out (rough) HP at the wheels numbers. i.e. my own road Dyno.
But I assume perfect traction on asphalt.
I like what you’ve done here.
Really informative piece. What do you know, my math and science teachers were right: I did find all that learning useful, especially for reading your article.
Could you share this spreadsheet somewhere?? Put authorship information in the sheets,but I would love to mess with it!
I was told there would be no math.
Someone lied to you.
Oh man, just wait for my next piece. You haven’t seen math yet.
Show them some differential equations.
Don’t make me go through Navier Stokes again, please!
This is also why Bowser has the highest top speed in Super Mario Kart.
I assume.
Turtles are also more aerodynamic than plumbers or princesses. The drag coefficient of Peach’s dress must be over ten RuPauls per square meter!
This here is the math behind “quick” vs “fast”.
Was just reading early Autopian yesterday and hoping for more articles from you. Many thanks
The ground effect article and now this? Are you gunning for my job Huibert?
Excellent read as always though!
Many years ago my friend and his father took a 1956 Lotus Eleven to Bonneville and went 143mph. The Eleven is known for aerodynamic efficiency but also light weight. They constructed a completely covered cockpit from Lexan to make it as slippery as possible and changed the final drive gear to allow 150mph top speed. When they got there they realized they needed one final modification – in order to get enough traction on the salt, they had to fill the DeDion tube connecting the rear wheels with concrete!
Lol! Perfect! they added weight and put it all right over the drive wheels. Brilliant.
I’m curious about what would be the most common limiting factor for the 400+ “normal production” cars at SpeedWeek.
i.e. what is the biggest barrier for most common folk?
Poor aerodynamics, lack of horsepower, inadequate tires, mechanical failure, inappropriate driver input?
Or just a wide variety of everything?
A “normal production” car would never get there because there just isn’t enough traction on the salt to overcome the drag. Maybe if it were on pavement you could do it, but salt is just too slippery.
If you want to make your LSR car accelerate quicker and stick to the ground better, without adding mass, could you not build a fan car? Probably not the best idea on a salt track, though perhaps some sort of filtration system could be designed. Just spit balling here.
Whatever filtration you had would quickly plug up but more importantly, the fan would still suck energy away from the engine. If you had power to spare it might work though.
More spit balling! If you can’t suck salt, could you not blow? Admittedly there is no seal with the ground to create suction, but would it not be possible to use extra power – or waste heat and exhaust gases to – generate downforce without adding mass? Do any of the LSR cars aim their exhausts skyward for this purpose?
Yes they do. Check out the first car in the Instagram post linked in the article. Those aren’t the real fast cars though. The real fast ones just point it rearward to hopefully get some forward thrust.
Like the Chaparral 2J, one would probably want a second power source for the fans, plus not having to connect it to the drive power would offer more freedom for designing ducting. Of course, this wouldn’t be useful on salt, either way.
So as I understand it:
In the 3000 pound RWD production car with sufficient horsepower example, It would essentially turn into a drift car as the rear tires lose traction.
AND this is happening at 180 mph on the salt flat. Cool.
That would certainly be an underwear discoloring situation for most people.
Is there a practical limit to how wide a tire can be on something so purpose built?
i.e. does rolling resistance or some other factor outweigh added traction enough to decrease top speed/increase acceleration distance?
I don’t know but I imagine there are limits based on the stresses inside the tire at those high speeds. A drag race tire is very wide, but it also grows a lot at speed. That wouldn’t be good in a LSR car where you don’t want the car lifting up nor do you have the space for a tire that has grown significantly in diameter.
My understanding from years of seeing team interviews, car engineering and the like is that the goal is to see how narrow of a tire you can run vs how wide. Really concentrate your weight on as small of a contact patch as possible.
Many, many versions of “the push truck will get you to 50, so you don’t worry about starting grip.”
Unless there are multiple Studebakers that go out to the salt flats I saw that getting rebuilt before the first time it went out there. The guy who made it started the project with the explicit goal of making a 200mph Studebaker (and succeeded if I remember correctly).
There ARE multiple Studebakers that come tom Speed Week but that one is still very cool. Also, they tow it with an early 50’s era Mayflower moving van!
Excellent stuff, Huibert!
I was expecting the answer to involve something like “carbon fiber shattering into a bajillion pieces if there’s a crash”.
I still kind of wonder if carbon fiber’s tendency to fail catastrophically when it fails is a factor, even if it’s not the primary one. A lighter body would let you put more ballast down low to end up at the same weight. Maybe that isn’t a limiting factor though.
OMG that’s some deeply thought out stuff here. A well written explanation of a bunch of factors that must be considered as both variable and absolute at the same point in time. Thank you for this.
But my cousin says you can get another 5 mph top end just by removing the A/C compressor and the spare tire.
Your cousin is partially right. Keeping the AC off will help top speed by not robbing power from the engine but removing it will do very little. Removing the spare tire will do nothing for top speed but will let the car get there sooner.
Any remotely modern car will turn off the AC compressor at wide open throttle anyway.
Very interesting! Based on this model, does the coefficient of friction on the salt make a significant difference in speed? My assumption is that lower speeds would be more effected my “stickier” salt where higher speeds would be negligible
The coefficient of friction of the tire is critical to this whole thing. More friction means more force from the tires without having to add weight.
Fantastic article. I was captivated the whole time. Very cool. Side note, I would drive that lead photo car as my daily. That thing is just so cool.
Yes it is!
Agreed, the blue car in the lead photo makes me feel things. Does anyone know the name of it so I can try to look up more about it?
That car is the 1929 Ford Roadster owned and run by Erik Hannson in the Blown Gas Roadster class. For some reason he parked that puppy in exactly the right spot on the salt for that shot. Thanks Erik!
This is fascinating. We non-engineers out here have very little clue how to quantify the tradeoffs involved. And now I am wondering about underbody aero that could pull the wheels down without the huge drag of a wing…
I don’t know a ton about aerodynamics (I am an engineer, but stayed away from that side of campus), but I’d imagine that fundamentally any aero that adds downforce is going to add drag. You could make it more or less efficient at producing downforce at a certain speed, but at the end of the day that force has to come from somewhere.
You are correct. The energy that is pulling the car down, no matter how the downward force is created, has to come from somewhere and the only source of energy in a car is the engine.
This is a very good way to explain it.
Solid article, good job!
Which leads us to the innovation of the fan car, where you can add downforce without affecting the drag
True, but the energy to run the fan also has to come from somewhere. You could run an electric fan from a separate battery (more weight!) but otherwise you add drag to the engine via the alternator.
Separate systems and the weight would help if located over the driven wheels.
I had never realized that about LSR cars. Very cool to see how the inputs affect the acceleration.