By going to a wider tire, you increase the footprint and the frontal area, both increasing drag .

*[Editor's Note: This article appeared in the December 2013 issue. Some information may be different today.]*

**Story by J.G. Pasterjak • Photography as Credited**

Friction is what makes tires fun. The more they generate and the more grip they have, the more smiles they put on our faces. But that same friction that helps us cling to the road when clipping apexes also slows us down when we’re on our way to the track.

How much energy are we expending just to move those sticky tires over the road? Are modern high-performance tires–the ones so capable on the track or autocross course–killing our fuel economy? Do we care?

When we asked ourselves that final question, we didn’t have a good answer. Anecdotally, we had a feeling that stickier tires cost us a few mpg. Probably. Maybe. But we at least wanted to objectively measure what we were up against.

So we called someone smarter than we are (it’s a thick book): our old pal Steve Stafford. Steve’s forte is aerodynamics, and you’ve probably seen his stories in previous issues. He’s the man with the math when it comes to all things drag.

And we even had the perfect test mule for the project in the form of our 2013 VW Beetle TDI project car. The TDI’s strong suit is delivering high fuel mileage thanks to an efficient engine driving an aerodynamic package with low rolling resistance. Routine driving typically put us near 45 mpg on the OE tires, so we wanted to know if upgrading the rubber would downgrade the economy.

The anecdotal data showed that it did. The Beetle TDI comes equipped with a set of 215/55R17 Continental ContiProContact all-season tires. At 26.3 inches in diameter, they’re relatively tall for such a small car and somewhat narrow by today’s standards. We replaced them with a set of 245/45R18 BFGoodrich Super Sport AS tires. We were simply looking for a more sporty footprint and compound while keeping a similar overall diameter in hopes of retaining some of the fuel economy.

According to our fuel and mileage calculations, our average consumption dropped by 2 mpg, from 40.2 to 38.2. Mileage calculations can be tricky, though. Ours were done under “real world” conditions, and countless variables can easily sway those numbers: too much time spent at red lights, heavier-than-usual traffic, etc.

We simply don’t have the time to drive 1000 miles under controlled conditions to get exact mileage readings because we’re too busy making magazines. However, we do have the time to do some coast-down testing. We simply found a stretch of road–we mean, uh, a closed controlled course–where we could accelerate safely to 60 mph and then let the car decelerate to 30 mph in neutral. We measured the time needed for each coast-down run, and took several passes each way to cancel out the potential effects of wind and slope. Then we averaged the results and sent them to Steve.

Here’s where Steve’s magic formula comes in. Rather than try to paraphrase his response, we’ll just print it below. Maybe his demon magic will make sense to the non-English majors out there. For everyone else, don’t get scared off by the math because if you skip ahead you’ll find a cheat sheet of sorts.

We’re trying to figure out the force of drag (F). Since we know how much the car weighs (which gets us m) and we have the deceleration (a)–or at least the data to calculate it–we can solve the simple equation: F=ma.

Since we’re talking about testing the car on a relatively flat surface–or, in this case, averaging the data in opposite directions on the same surface–we can assume that the mass of the car acting against the drag is the weight of the car converted to mass.

To convert the car weight to mass, we need to divide the weight of the car, in pounds, by the gravitational acceleration. The gravitational acceleration for our purposes can be approximated at 32.2 ft./sec.2. [Ed. note: It varies with altitude; ask your local astronaut.]

This converts the weight of the car in pounds to the mass of the car in slugs. [Ed. note: Really, who comes up with these unit names?]

The acceleration is the difference in speed divided by the time between the two speeds.

The speeds from the start and the end of the deceleration need to be in ft./sec., not mph, so we’ll multiply our speed in mph by 1.466667.

The deceleration time needs to be in seconds and as accurate as you can get. Here’s the formula for deceleration: (starting speed–ending speed)/deceleration time.)

The deceleration is effectively a negative acceleration, so throw a negative sign in front of it, and the units are now ft./sec.2. For a relative number, you could divide the deceleration by 32.2 to get the g-load.

Now we have everything we need to calculate the drag force.

The output of F=ma will give a force in pounds.

This force is the average force on the car from your starting speed to your ending speed. Put another way, it’s the drag at the average speed.

This drag force is going to include everything from aero and tire resistance to bearing drag and any slopes in the road (which were eliminated by doing multiple passes in both directions).

Now we can convert that drag force in pounds to an equivalent horsepower. The basic formula is: horsepower=torque*rpm/5252.

Since we don’t have the torque or the wheel rpm, we need to calculate them.

We generated the drag for a given coast-down speed and need to convert it to torque at the drive wheels before we can convert it to horsepower. The only additional measurement we need to do this is the rolling radius of the tire.

Let’s take a wild swing and say the rolling diameter is 12.5 inches. That gets converted to feet by dividing by 12, giving us 1.04 feet.

The torque required to equal the drag is calculated by multiplying the drag force by the tire radius. This will be a pretty large number in relation to engine torque, but we have lots of gearing to amplify the engine torque as it makes its way to the ground.

Now that we have the torque at the ground, we need to use the speed conversion from the coast-down side to get the average speed in ft./sec. The average speed between 50 and 30 mph is 40 mph; converted to ft./sec.,

it’s 58.67 ft./sec. (multiply mph

by 1.46667).

We need the circumference of the tire as well. That is the rolling radius multiplied by 6.28 (gives the diameter*pi). Do this for the value in feet so you don’t have to convert units.

Knowing the speed and the circumference, we can determine the rpm of the wheel. Since we know how fast the tire is moving along the road and how far one rotation of the tire will take us down the road, we can get the rpm by dividing the speed in ft./sec. by the circumference in feet and multiplying the whole thing by 60 (because there are 60 seconds in a minute; otherwise we’d wind up with revs/sec.).

Now we have all the numbers we need to get the horsepower (at the wheels) needed to overcome the drag on the car.

Following the formula, multiply the torque by the rpm of the wheel and divide the whole thing by 5252.

Out pops the horsepower, at the drive wheels, required to keep the car running at the average speed of the coast-down run.

For those of you who don’t want to go back to school, we made things easier. If you go to grassrootsmotorsports.com/coastdown, you can download an Excel spreadsheet that does all the math for you. All you have to do is plug in the car weight, starting and ending speeds, time elapsed, and tire size. The spreadsheet will magically compute your own coast-down calculations. This is a great tool for determining not just rolling resistance, but aero drag as well, since the formula measures total drag in the system. You could even get crazy and use this formula to measure the effect of weight or driveline drag on a car’s performance.

Once we crunched our numbers for our TDI, we learned that, with our OE Continental tires, we were producing an average drag force of 88.25 pounds during our coast-down, or the equivalent of 10.6 horsepower. Our high-performance BFGoodrich street tires pushed that up to 98.51 pounds of drag, or the equivalent of 11.8 horsepower. That’s basically a 10-percent increase in tire drag, which made our 5-percent decrease in fuel economy completely believable.

Then we threw on a set of sticky BFGoodrich g-Force R1 race tires and repeated the test. The 245/40R18 R1s pushed our car’s total drag to a whopping 124.58 pounds of drag, or the equivalent of 15 horsepower. They do stick to the road, but obviously they’re costing us some straight-line speed.

For a little perspective, we took our Beetle to Virginia International Raceway to run it in the Ultimate Track Car Challenge and conduct some tire testing. We basically knew how the tires would finish on track, we wanted to see how much additional grip we were getting for our mileage tradeoff.

Although the finishing order was predictable, the results were still interesting. The OE Continentals were the slowest at an average of 2:39.1. They still provided a good bit of drivability, though. While they wouldn’t be our first choice for a track tire–that wasn’t what they were designed for–they held up admirably and provided good feedback regardless of their stated mission.

The BFGoodrich Super Sports were predictably faster by a full 2 seconds. Additional width and a more aggressive compound did their thing to improve lap times. In both cases of the street tires, though, lap times were held in check as much by the non-defeatable stability control as by the tires. While the intervention was not unsettling, we were definitely aware of its presence at times.

Fastest of all–not surprisingly–were the BFGoodrich R1s. They were more than 7 seconds faster than the Super Sports and nearly 10 seconds faster than the OE Continentals. Even more impressive, though, was the way the R1s seemed to work in concert with the stability control to turn it into an asset instead of a liability.

Our best guess is that the stability control is highly affected by slip angle and yaw rate, and the lower slip angles and yaw rates at which stickier tires naturally work are a much better companion to the digital overlord under the dash. There were more than a few times when we were heading through the uphill esses or into Hog Pen and getting ready to countersteer–to catch a slide or adjust the throttle to bring the car back on line–and the Beetle beat us to it. And it did so while losing an absolute minimum of momentum. Kudos to VW for designing a stability control that doesn’t punish us for having a little fun now and then. We’d still prefer an off button, of course.

So now you understand some of the tradeoffs a bit better between grip and grin. Those sticky tires will give you a great deal more grip in the corners, but they’ll also cost you power on the straights.

There is a ton of anecdotal data about this out there if you look at drag racing. Drag slicks are well known to 'eat mph' and if you know your race weight and before and after trap speeds it's pretty easy to ballpark some power consumption numbers. Now in that case a lot of it comes down to sidewall deflection and the very stick compound is probably in 2nd. In street tire terms I think the mpg loss is MOSTLY attributable to aero impacts from the front tires with actual rolling resistance being secondary.

Another stark way to find the losses from tire 'upgrades' is to see the kind of range that EVs lose when you put 'autox tires' on them. It's considerable..

Wider tires can cost you top speed due to increased drag and turbulence, but a lot depends on the individual car. Miatae (in stock form anyway) have almost no front bumper or fender coverage of the tires, they just hang out in the wind. Other cars are better considered in this regard and probably pay less of a penalty at high speeds.

My s2000 with 255 Bridgestone re71r tires and an aggressive autocross alignment loses about 3-4 mpg on the highway compared to normal tires and a modest alignment. The effect is real.

It also doesn't appear you weighed the tires to see what effect that would have. Heavier tires take more energy to spin up to speed (remember, all cars have 5 flywheels: one on the engine and one on each corner)

It seems a better test would have been to stay as close as possible to the same tire size and weight and only adjust the compound. Introducing two extra variables isn't very scientific.

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