NASCAR PHYSICS: How Drivers Are Going To Get Around A Flat New Hampshire Track

Nascar Physics
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NASCAR is heading north this week for some more short-track racing at New Hampshire Motor Speedway. The Magic Mile is a flat, progressively banked, one-mile oval located in Loudon, NH. 

After hosting the Xfinity (then Busch) series for three years, Loudon was first visited by the Cup series in 1993. Prior to the 1997 season, Bruton Smith of Speedway Motorsports, and New Hampshire Motor Speedway developer Bob Bahre purchased North Wilkesboro Speedway. By purchasing the speedway, the pair were able to shift one of North Wilkesboro’s dates to New Hampshire, giving it two Cup series races annually. Loudon was visited twice per year by the NASCAR national series from 1997 to 2017, before losing its fall race to Las Vegas Motor Speedway in 2018.

New Hampshire Motor Speedway is also indirectly responsible for the “lucky dog” or “free pass” rule that we race with today. In 2003, it was NASCAR’s policy to allow drivers to race back to the start/finish line to begin a caution period. The purpose of this policy was to allow drivers one or more laps down to attempt to pass the leader and get their lap back before the caution. On lap 159 of the 2003 Sylvania 300, Dale Jarrett crashed and came to a stop on the front straightaway directly in the path of drivers coming along at full speed attempting to get their lap back. Luckily, everyone avoided contact, but it was a close enough call that beginning one week later at Dover Motor Speedway, NASCAR would freeze the field at the time of caution and the first car one lap down would automatically get their lap back.

It’s unfortunate that we only come to New England once per year but race fans are in for a treat this weekend. If you’ve been following these articles from the beginning, you’ll have noticed that we spend the majority of our time talking about tires. Shocker, this week is no different. Short, flat tracks cause the vehicle to have a tendency towards oversteer on corner entry and understeer on corner exit. Let’s dive into why. 

It’s Tire Time Again

Every tire has what’s known as a lateral force coefficient (LFC), which defines the relationship between the tire’s lateral force capacity and the vertical load applied to it. The LFC can be calculated by dividing the lateral force by the vertical. 

Tire Graphic
Source: Milliken and Milliken SAE

As you can see, increasing vertical load increases lateral force capacity, but the relationship isn’t quite as straightforward as it initially appears. If we take the same data set and plot the LFC instead of just the resultant lateral force a different story begins to emerge.

Tire Graphic 2
Source: Milliken and Milliken SAE

There are two things that should be noted from this rearrangement. First, the slip angle at which peak lateral force is generated is dependent on vertical load. Secondly, the LFC actually decreases as vertical load increases, indicating a non-linear and diminishing relationship between load and cornering ability. Essentially, if adding 100lbs of load adds 100lbs of cornering ability, adding 200lbs of load will produce 190lbs of cornering ability. Every pound of load added produces slightly less grip than the pound before it.

Flat As A Pancake

That’s cool and all, but you may be wondering why I waited until this week to break out that tidbit. The answer has to do with the flat nature of Loudon’s corners. Everyone knows that more banking allows a car to go faster around a corner, but let’s break down why and how it affects a car going around a circuit. The maximum speed of a car going around a banked corner is governed primarily by the coefficient of friction and the banking angle. As the banking angle increases, a larger and larger percentage of the force holding the car on its intended path is supplied by the normal force (N) which acts perpendicularly to the track surface. For the nerds amongst us, here is the free body diagram and corresponding derivation. For the rest, I’ll explain what it means.

Hyper Physics Banked
Source: Hyper Physics Lab

Let’s work this out for Loudon. Using a coefficient of friction of 1.0, a corner radius of 450 ft and a banking angle of 5* the Vmax works out to 85 mph which is about what you would see a driver running at on sticker tires. Now, if we increase the banking angle to 24* like we would find at Dover Motor Speedway, also one mile in length, this Vmax number would increase to 132 mph. Okay yes, this much is obvious, more banking equals more speed. If you still aren’t seeing how this would change the racing product, stick with me.

Now there are a lot of differences between Dover Motor Speedway and Loudon, one is concrete and one is asphalt for example, but let’s focus on the banking. Corner entry speeds at Loudon are in the neighborhood of 155 mph, and we just worked out that the mid-corner speed is around 85 mph on fresh tires. This translates to a 44% reduction in velocity. If we cranked up the banking angle to 24*, and increased the corner speeds to 132mph it would only be a 15% reduction in speed. That’s interesting, because looking at driver data from Dover, where drivers enter the corner at around 170 mph and slow down to 145 mph mid-corner, that is also a 15% reduction in velocity.

Flat Racing
Photo: Big Machine Racing/Daylon Barr Visuals

Not only does steeper banking increase mid-corner speeds, it also closes the gap between minimum and maximum velocity over the lap. More banking produces what we call momentum racing, where there is minimal acceleration and deceleration. The focus is on being smooth and keeping your momentum up with as little off-throttle time as possible.

On these higher-banked tracks, the car achieves a semi-steady state once it has entered the corner. At flatter tracks, with a significantly larger difference between minimum and maximum speeds, the car goes through much more dynamic transitions as drivers brake hard on entry, pivot in the middle, and then launch onto the next straightaway.

Instead of being pulled down squarely into the banking the car pitches and rolls its way around the corner. These harsh weight transitions make setting up a car for a flat track quite tricky for race teams. Their three priorities going to Loudon will be entry stability, center rotation and exit traction.

Let’s look at how weight transfers on a car as it goes around a flat corner. During the braking phase weight is shifted evenly from the rear tires to the front tires. When the driver turns into the corner, the weight is shifted both forward and to the right. As the right front tire loads up, the car will want to cut hard into the corner and the underloaded rear tires can struggle to keep up. Having weight biased towards the front, and no banking to lean on, is what causes the sensation of corner entry oversteer. You can see below as Alex Bowman loses control of his car on the entry to Turn 1 during practice for the 2019 Foxwoods Casino 301.

One of the biggest struggles in short-track racing is getting the car to “roll the center.” This is the phase mid-corner when the driver is coasting, off of both pedals, trying to get the car far enough around the corner that they can begin applying throttle. When free rolling there is no front to rear weight transfer, but the car is now at its maximum lateral acceleration. Without banking, almost all of the lateral force acts horizontally on the car. Instead of being pulled down into the racetrack, the forces try to roll the car towards the outside. Remember, lateral force is generated at the contact patch but acts on the car at its center of gravity (CG). In this part of the corner, the right-side tires will be overloaded and the left-side tires will be underloaded. Minimizing body roll and keeping load on the left front tire are crucial to getting the car to rotate through this phase of the corner.

On corner exit, drivers will have to contend with the opposite scenario that they faced on entry. As they accelerate off the corner, weight will be shifted towards the right rear corner. With weight biased towards the rear, those tires will be amply loaded for acceleration and the front tires will be underloaded for cornering, creating understeer.

A secondary problem created by corner exit understeer is snap oversteer. As the car pushes on corner exit, drivers will naturally add more steering angle to try and correct it. The graph below shows the relationship between slip angle and lateral force for a generic tire. Lateral force increases with added slip angle up to a certain point when grip falls away as the tire begins to slide. If a driver is struggling with understeer, it is very easy for them to end up on the back side, downward sloping, part of this graph as they are operating past the optimum slip angle.

Tire Banking Graphf
Image: Paul Haney, The Racing and High-Performance Tire

The snap oversteer is created when a driver begins to unwind the steering wheel as they exit the corner. It’s counterintuitive, but if you’re operating past the peak slip angle, reducing steering input will generate more cornering force. So as the driver exits the corner and straightens the wheel, the front end of the car will “grip up” and can create a moment of snap oversteer late in the corner.

At New Hampshire Motor Speedway, 46% of the racetrack is made up of the corners. There is no place to hide if you’re struggling and no amount of power will make up for it down the straights. Teams will try to combat this weight transfer and body roll in a number of ways. One of the most effective ways will be in lowering the cars CG. You can read more about that in my piece from Martinsville Speedway.

Lowering the CG height is always a net positive, but every other change to the vehicle has pros and cons to them. Increasing right rear spring rate will keep the car pitched down onto the left front, but will create oversteer on corner exit. A pair of softer rear springs will have more traction on exit, but they will pitch more weight onto the nose under braking. A bigger sway bar will reduce body roll but create understeer mid corner. You see what I’m getting at. As I like to say, there are no free lunches in racing, and setting up a car is all about balancing out the pros and the cons.
Damper selection is also crucial to making lap time around the Magic Mile. Loudon has a road course layout that is often used for Legends Car and SCCA racing as well as driving schools.

Nhms Track Map Please
Source: NHMS

The entrance and exit of the road course loop are right before the entrance to Turn 3 on the oval layout. Over the years this has worn the surface in to create a series of bumps in the braking zone. A car will cross over these bumps at the same time as the rear end is becoming unloaded by the braking forces. If the springs and dampers aren’t properly timed to one another, the bumps will unsettle the rear of the car and cause significantly more corner entry oversteer. In this replay you can see as Jimmie Johnson’s car rides over the bumps, the rear of the car begins bouncing and he is never able to regain control.

The Xfinity and Cup series cars both have to deal with these bumps, but the cars react in much different ways. Xfinity series cars are what’s known as “ride height cars” meaning that they have to go through technical inspection and be able to hold themselves up at a minimum front and rear ride height. On the front of the car, teams are allowed to utilize bump stops. These are simply metal springs that fit around the damper shaft. Teams design the front of the car to be just soft enough to hold itself up statically and allow it to ride around on the bump stops the whole way around the track.

The bump stops typically catch the car within an inch of bottoming out and so their spring rate can be quite stiff. In the rear of the car, no bump stops are allowed, so the conventional suspension springs must be soft enough to allow the suspension to travel down on its own. This means that the wheel rates of the front suspension are typically much stiffer than the rear wheel rates. The car will be pinned on the front bump stops and the rear suspension can bounce around much more on the softer traditional springs, making it even harder to get the car to handle properly through the bumps. Picture a pickup truck pulling an empty trailer down a dirt road. The truck at the front will be firmly planted to the ground while the trailer in the rear will be bouncing all over the place.

The progressive banking at Loudon helps to produce tons of compelling, side-by-side racing. It may be hard to see visually, but at a track this flat and fast, any added banking angle creates a noticeable amount of grip. Drivers running the middle groove will be travelling further but with more banking and drivers running the extreme inside will take a shorter distance with less banking. The outside groove is traditionally preferred both for racing and defending.

A driver attempting a pass will take the inside line into the corner and try to nose ahead by the apex. They can run an aggressive diamond line and slide up in the middle, forcing the defending car up the racetrack in the middle. The defending driver will try to combat this by holding their lane and pinching off the overtaking driver as much as possible on corner exit. It often takes several corners to complete a pass as drivers work each other over inch by inch until they are eventually able to clear themselves.

Keep your eyes open for all the different strategies this weekend and enjoy some great New England-style short-track racing.

Photo: Big Machine Racing/Daylon Barr Visuals

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15 thoughts on “NASCAR PHYSICS: How Drivers Are Going To Get Around A Flat New Hampshire Track

  1. Awesome article, and I usually don’t care much about technical racing dives like this.
    Also, I’m from New Wilmington PA and had a good friend who was in charge of PR for JR racing when Brad was breaking in. She has since moved back to PA, but if you knew Martha you know!

  2. I am loving these articles. I hope that most readers are like me: Reading, learning, thinking, saying “huh,” thinking some more, reading again, and getting smarter about it… all while having nothing to say. I’m really just posting now to prop up the engagement numbers and to thank McHugh for writing such clear-headed pieces.

  3. The Cup race on Sunday had some interesting moments. After the 2-hour + rain delay, they went back to racing on wets, with a fairly wet track. Right away the dirt-track guys went to the front of the pack. Everyone drove all over the track, seeking dry and then seeking wet to cool the tires as the track dried and the tires blistered. NASCAR micromanaged the pit stops, which was a mistake. Should have put the wets on and let’em race.

  4. Great article again Aedan. You reveal a lot of the complexity behind what can look like cars just driving in circles. Is there any public knowledge of what setups teams choose for a particular race? Or is this a closely guarded secret? Also, do you think most teams run fairly similar setups at a given track?

  5. The overlap between the cheap beer swilling crowd that likes NASCAR and people who remember some high school level math has be to be very close to 0.

      1. Sigma notation came up for a select few in my high school at least. This isn’t the geometry or Algebra II where most people tapped out in my neck of the woods, and I would hazard a guess that’s true of many other places.
      2. I am not even big on NASCAR but I love love love these articles and appreciate Aedan putting in the time and effort, writing about each track and what makes it different, or the same as other tracks. I appreciate that The Autopian keeps running them even though they’re flanked by higher engagement (at least by comment count) posts every weekend.
      3. I’ve been well-boozed at an IMSA race, and when I’m watching them nail turn after turn for hours on end with unreal precision, I’m not judging myself, the drivers, or anyone else about the math classes they do or don’t remember.
      4. This is a great chance to reach across that divide and connect with the cheap beer swilling crowd. I’m still kicking myself for not going to Richmond, and when I’m working I’m going to try to get to at least a little NASCAR entirely because of these articles. Or, if it really just isn’t for you, you don’t have to look down your nose at those that do enjoy it. I get it, I would have done and did do the same thing when I was younger. I know better now.
    1. Agree w Mechjaz and Lizardman. Vectors aren’t hard to understand even if you can’t translate them into math expressions. It just gets described in different language: On one of the vids above, you hear, “he couldn’t get it turned.” That about says it.

  6. So from a strategy pov, it sounds like the outside line, with more banking, is preferred b/c it smooths out the tenor of all the various inputs a driver needs to make so at least statistically, less chance of problems? So then the inside lines are higher risk, but what a driver needs to use to make a pass…

    I feel short tracks are way underrated for the actual racing drama they provide.

    1. I feel short tracks are way underrated for the actual racing drama they provide.

      I’m not trying to be rude, but how long have you been following NASCAR? Short tracks have always been regarded as the best tracks for actual racing all the way back since I started watching in the 90’s. They’re far from underrated, even if this new “next gen” car struggles a bit on them.

      1. Since about the late 90s, when I moved to a place where I could actually see it (I grew up in the midwest, so racing was pretty much only Indy/CART)!

        Excuse my imprecision – I meant in terms of the average viewer. It’s been cool to watch the company of Nascar work to grow the sport’s reach over the years, but it does seem like it tries to focus attention mostly on the superspeedway events, I guess b/c high speeds and dramatic wrecks. But things seem to be shifting – more road courses, etc – so the continued evolution seems to bode well for the future.

  7. I wish I could remember where I read it – to quote “Tommy Boy,” too much malted hops and bong resin – but I read about an early NASCAR race on a much flatter non-NASCAR track that didn’t have nearly the banking that Talladega or Bristol or Daytona has. On day one, many of the drivers came into turn three as hot as they would in one of those places, and an observer was quoted as saying, “They’re going over the wall. They’re *all* going over the wall.”

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