The Science of …G-Forces

UPDATE 4/18/08: NASCAR.com has a very nice interview with Dr. Dean Sicking of the University of Nebraska-Lincoln about the SAFER barriers and how they functioned during the McDowell crash discussed below.

As the FedEx commercials say, “The questions keep rolling in…”

Tim King asks, “One thing I have been trying to get ever since the installation of the black boxes are the G forces measured during the impacts. Nothing is published that I can find. Any suggestions?“

Michael McDowell’s qualifying accident is still in the news as NASCAR continues to analyze the event. Their analysis is very important for them to understand what happened and how the new car responded.

How do you quantify how ‘bad’ a crash is? Thankfully, there have been very few injuries in NASCAR crashes in recent years, so we don’t measure the seriousness of a crash in broken bones and bruises. Cal Wells of Michael Waltrip Racing noted that the crash wasn’t “as bad” as that experienced by Jeff Gordon at Las Vegas when he hit a wall that didn’t have SAFER barriers. As reported by SceneDaily, Wells said:

“It wasn’t as big a hit as the 24 took. The 24 hit a concrete wall and it jerked the motor and the transmission. … Everything [on McDowell’s car] performed extraordinarily close to design.”

That’s a fairly subjective evaluation of the crash. The same SceneDaily article reported comments from John Darby, the Sprint Cup Series Director. I’m quoting Jayski’s article verbatim here for a reason.

NASCAR still evaluating McDowell’s car and data: G-force readings [no number given] from #00-Michael McDowell’s grinding crash at Texas Motor Speedway last weekend were lower than other major wrecks in NASCAR, but Sprint Cup Series Director John Darby said the nature of severe crashes in the new car has changed so much that G-force readings don’t mean as much as they once did. NASCAR has begun the process of thoroughly examining McDowell’s battered Michael Waltrip Racing Toyota in its Research & Development Center, Darby said, adding that the G-force numbers were “pretty low.” But that wasn’t totally unexpected, because the design of the new car and the SAFER barrier has changed crash dynamics. “G-forces overall have been reduced,” Darby said. “But when you look at the big picture, the G-force is the least significant number anyway.” The significant number is the change in velocity, which Darby said was “substantial” with McDowell’s car. “They weren’t the worst we’ve ever seen by any means,” Darby said. “But part of the process of building a safer race car is to reduce all those numbers as best we can. Even when we understand completely the final numbers – which ultimately will be lower than what we’ve seen in the past – that’s what we’re looking for.” (SceneDaily)

So what’s a “G-force”? A ‘g’ (I’m used to using the lower case) is a unit that measures acceleration. Acceleration is how fast your speed changes, as described by the equation below.

One ‘g’ is 9.8 meters per second per second (which is 32 feet per second per second in British units), which is the acceleration due to gravity. If you were skydiving (ignoring the effects of air resistance), your speed would increase by 9.8 meters per second each second you were falling. After one second, you would be traveling 9.8 meters per second. After two seconds, you’d be traveling 19.6 meters per second, and so on.

I’ve had a number of questions from people about how you can use a ‘g’ to specify an acceleration in a direction other than down, since ‘g’ refers to gravity. A ‘g’ is a unit for acceleration just like a yard is a unit of distance. You can travel a yard in any direction. Similarly, you can accelerate in any direction. If you are accelerating at 25.0 meters per second per second, your acceleration is 25.0/9.8 = 2.55 g. It doesn’t matter what direction you’re accelerating in. The ‘g’ is just convenient.

To get the force, you have to multiple mass times the acceleration.

Right now, you’re experiencing an acceleration of 1 g due to Earth’s gravity. The force corresponding to this acceleration is your weight, which is one ‘g’ times your mass (in kg). In the British system of units, we don’t often talk about mass (which would be measured in an archaic unit called a ‘slug’). We talk about weight, which is in units of pounds (lbs). When you talk about an acceleration of 3gs in the British system, you’re talking about a force that is three times the person’s weight. When you hear that a box measured ‘5gs’, it measured an acceleration of 5gs, not a force of 5gs.

The problem with quantifying crashes using force is that the force you experience depends on your mass. That makes it hard to compare incidents with two different people. The force corresponding to 3gs for Michael Waltrip (who weighs 210 lbs) is 630 lbs, while the same acceleration produces a force of 450 lbs for Jeff Gordon (who weighs 150 lbs). Accelerations allow you to compare two different collisions.

If you combine the two equations above, you get the equation that is the fundamental basis of accident analysis.

The first thing you’ll note in Jayski’s summary is the “[no number given]”. NASCAR doesn’t release the accelerations measured by the “black box” transponders. As John Darby said, “…when you look at the big picture, the G-force is the least significant number anyway.” It isn’t that the number is meaningless: It’s that there is so much more to a collision than the acceleration experienced by the black box. The transponder measures the acceleration experienced in one specific area of the car.

The driver didn’t necessarily experience the same acceleration. The seat, the position of the seat with respect to the car, the harnesses, the helmet and the HANS device give the driver protection that the transponder doesn’t enjoy, and some of the energy of the collision is dissipated in the destruction of the car. (In some racing series, the drivers wear small accelerometers in their earpieces, and those instruments provide a more direct measurement of the acceleration of the driver’s head, but those numbers still don’t reflect a variety of other variables that are equally important.) The accelerations measured in the new car can’t be compared directly to those measured in the old car. The new car has a much different chassis design and an entirely new door design, so it shouldn’t be surprising that the accelerations measured are less in the new car. Finally, in a collision like McDowell’s, the driver experiences multiple forces. He experienced a force each time he hit the wall, each time the car spun, and each time the car hit the track while it was tumbling. The black box number usually corresponds to the largest force.

There are two factors that determine the force experienced in a collision. The greater the change in velocity, the greater the force; however, you also have to take into account the time over which the change in velocity occurs. Let’s assume two drivers change their speeds from 180 mph to rest. They both have the same change in velocity (which we call ‘delta v’, ‘delta’ meaning change). If one driver has a hard crash into a non-forgiving wall and we assume that the time over which the collision occurs is 0.1 s, the acceleration he experiences would be 2640 feet per second per second, which corresponds to 82.5 g. If the second driver comes to a stop during a long skid that takes 2 seconds, the acceleration would be 132 feet per second per second, or a little more than 4 g. The SAFER barriers extend the time of collision. Let’s say our first driver hits a SAFER barrier instead of the wall and the time of collision is extended from 0.1 seconds to 0.2 seconds. The acceleration is 1320 feet per second per second, or 41.2 g. The accelerations recorded in Gordon’s Vegas crash were higher than those recorded in the McDowell crash because the time of Gordon’s collision was much shorter. McDowell changed velocity over a long period of time. When he hit the SAFER barrier the first time, his speed decreased some and he felt a force proportional to the ratio of the change in speed to the time during which he was in contact with the barrier. His speed continued to change throughout the crash and he felt forces throughout the crash. Gordon felt most of the force in the single collision he experienced.

If you’re interested in Darby’s comment about the importance of the quantity ‘delta v’, which the same as change in velocity, The Physics of NASCAR explains delta-v in more detail. Essentially, velocity is a vector, which means that it has a size and a direction, and it makes a big difference whether a car hits the wall head on or at a glancing angle.

The only times I’ve heard actual acceleration numbers made public was when drivers mentioned them and I know of at least two instances in which people familiar with the collisions told me that the drivers misheard or misunderstood the numbers, so I don’t place much faith in those numbers that do become public. The conspiracy theorists will claim that NASCAR just doesn’t want anyone to know; however, there is also an issue of respect for the drivers’ privacy, and the propensity of the media to sensationalize.

If you want to find realistic information about collisions, the best place to look is in the papers published by SAE International. SAE is a professional society for people working in automotive and aerospace industries. Safety researchers from around the world attend the bi-annual Motorsports Conference and present papers, many of which end up in the conference proceedings. Those papers, especially those published in earlier days, when we weren’t as sensitive to the release of personal data, often have real data from incidents that you can often match to names and places. I’ve found some very informative data like plots of force vs. time that give you significantly more information than a single number like a peak acceleration.

Safety is a much more complex problem than most people recognize. Every time there is an incident, there is a round of ‘why doesn’t NASCAR…?’, which is usually led by people who don’t appreciate that it’s not as easy as simply putting the same SAFER barriers that are on the outside walls on the inside walls. More about that next time.