# Lesson 4- Braking and Steering Dynamics

Lesson 4 of our SpeedScienceHQ website will focus on steering and braking systems. A driver's ability to steer a car with precision and slow it down effectively can make all the difference in a race. In this lesson, we will explore the science behind these two essential systems, including how they work, how they affect the car's performance, and how drivers can use them to gain an advantage on the track. We will also look at real-life examples of steering and braking systems in action, as well as the different technologies and setups used by racing teams to optimize their performance. Whether you're a newcomer to the world of motorsports or an experienced driver, understanding the principles behind these crucial systems is key to improving your skills and achieving success on the track.

## Steering and Braking systems

The Physics Behind Braking

The basic principle of braking is to use friction to reduce the car's kinetic energy, resulting in a decrease in speed. Brakes convert kinetic energy into thermal energy through friction between the brake pad and the rotor. The heat generated by this friction causes wear and tear on the brake pads and the rotors, which must be replaced periodically.

Stopping Distances and Deceleration The stopping distance is the distance covered by a car from the time a driver applies the brakes until the car comes to a complete stop. It depends on the car's initial speed, the driver's reaction time, and the car's deceleration. Deceleration is the negative acceleration of a car that slows it down. It is expressed in meters per second squared (m/s²).

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The formula to calculate stopping distance is:

Stopping Distance = Initial Speed x (Reaction Time + (Braking Force x Braking Time))

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For example, if a car is traveling at 80 km/h, and the driver reacts after 1 second, applies the brakes with a force of 1000 N, and the brakes can generate a deceleration of 4 m/s², then the stopping distance would be:

Stopping Distance = 80 km/h x ((1 second) + ((1000 N x 4 seconds) / (1000 kg x 4 m/s²))) Stopping Distance = 80 km/h x (1 + 1) Stopping Distance = 160 meters

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The String Theory and Examples from Racing

The string theory is the idea that the fastest way around a corner is to create a straight line through it. In racing, this means the driver must brake and turn at the same time to take the corner. This technique is called trail braking. By braking while turning, the car's weight shifts forward, creating more traction on the front tires, allowing the driver to steer through the corner.

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Brakes Lock Up and What it Does Brake lock-up is a situation that occurs when the driver applies too much force on the brakes, and the wheels stop rotating. When this happens, the car's tires lose traction, and the driver loses control of the car. The result is usually a spin or crash.

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How Does a Driver Cope with a Lockup?

The driver can cope with a lockup by releasing the brakes and then reapplying them with less force. The driver can also use the anti-lock braking system (ABS) to prevent lock-ups. ABS is a system that automatically modulates brake pressure to prevent the wheels from locking up.

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Inertia and Brake Inputs

Inertia is the resistance of an object to change its state of motion. When a car is moving, it has inertia, which means it will continue to move forward until a force acts on it to stop it. When the driver applies the brakes, the car's inertia resists the deceleration. The driver must apply enough brake force to overcome the car's inertia and stop it.

Physics Aspect of Trail Braking Trail braking is a technique that allows the driver to carry more speed through the corner. When the driver brakes while turning, the car's weight shifts forward, creating more traction on the front tires, allowing the driver to steer through the corner. The amount of brake force and the duration of the braking

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## Advanced formulations

.I was recently helping to crew Mark Thornton's effort at the Silver State Grand Prix in Nevada. Mark had built a beautiful car with a theoretical top speed of over 200 miles per hour for the 92 mile time trial from Lund to Hiko. Mark had no experience driving at these speeds and asked me as a physicist if I could predict what braking at 200 mph would be like. This month I report on the back-of-the-envelope calculations on braking I did there in the field.

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There are a couple of ways of looking at this problem. Brakes work by converting the energy of motion, kinetic energy, into the energy of heat in the brakes. Converting energy from useful forms (motion, electrical, chemical, etc.) to heat is generally called dissipating the energy, because there is no easy way to get it back from heat. If we assume that brakes dissipate energy at a constant rate, then we can immediately conclude that it takes four times as much time to stop from 200 mph as from 100 mph. The reason is that kinetic energy goes up as the square of the speed. Going at twice the speed means you have four times the kinetic energy because 4 = 22 . The exact formula for kinetic energy is ½mv2 , where m is the mass of an object and v is its speed. This was useful to Mark because braking from 100 mph was within the range of familiar driving experience.

That's pretty simple, but is it right? Do brakes dissipate energy at a constant rate? My guess as a physicist is "probably not." The efficiency of the braking process, dissipation, will depend on details of the friction interaction between the brake pads and disks. That interaction is likely to vary with temperature. Most brake pads are formulated to grip harder when hot, but only up to a point. Brake fade occurs when the pads and rotors are overheated. If you continue braking, heating the system even more, the brake fluid will eventually boil and there will be no braking at all. Brake fluid has the function of transmitting the pressure of your foot on the pedal to the brake pads by hydrostatics. If the fluid boils, then the pressure of your foot on the pedal goes into crushing little bubbles of gaseous brake fluid in the brake lines rather than into crushing the pads against the disks. Hence, no brakes.

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We now arrive at the second way of looking at this problem. Let us assume that we have good brakes, so that the braking process is limited not by the interaction between the pads and disks but by the interaction between the tyres and the ground. In other words, let us assume that our brakes are better than our tyres. To keep things simple and back-of-the-envelope, assume that our tyres will give us a constant deceleration of

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The time t required for braking from speed v can be calculated from: t = v / a which simply follows from the definition of constant acceleration. Given the time for braking, we can calculate the distance x, again from the definitions of acceleration and velocity:

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Remembering to be careful about converting miles per hour to feet per second, we arrive at the numbers in Table 1.

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Table 1: Times and Distances for barking to zero from various speeds We can immediately see from this table (and, indeed, from the formulas) that it is the distance, not the time, that varies as the square of the starting speed v. The braking time only goes up linearly with speed, that is, in simple proportion. The numbers in the table are in the ballpark of the braking figures one reads in published tests of high performance cars, so I am inclined to believe that the second way of looking at the problem is the right way. In other words, the assumption that the brakes are better than the tyres, so long as they are not overheated, is probably right, and the assumption that brakes dissipate energy at a constant rate is probably wrong because it leads to the conclusion that braking takes more time than it actually does. My final advice to Mark was to leave lots of room. You can see from the table that stopping from 210 mph takes well over a quarter mile of very hard, precise, threshold braking at 1g!

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## Advanced formulations - Trail Braking

. Trail-braking is a subtle driving technique that allows for later braking and increased corner entry speed. The classical technique is to complete braking before turn-in. This is a safer, easier technique for the driver because it separates traction management into two phases, braking and cornering, so the driver doesn't have to chew gum and walk at the same time, as it were. With the trail-braking technique, the driver carries braking into the corner, gradually trailing off the brakes while winding in the steering. Since braking continues in the corner, it's possible to delay its onset in the preceding straight braking zone. Since it eliminates the sub-optimal moments between the ramp-down from braking and the ramp-up to limit cornering by overlapping them, entry speeds can be higher. The combination of these two effects means that the advantage of later braking is carried through the first part of the corner. In many ways, this is the flip side to corner exit, where any speed advantage due to superior technique gets carried all the way down the ensuing straight. The magnitude of the trail-braking effect is much smaller, though: perhaps a car length or two for a typical corner. Done consistently, though, it can accumulate to whole seconds over a course.

When I was taught to drive in the '80s, not all the fast drivers used trail braking and instructors usually gave it at most a passing mention as an optional, advanced technique. The reason was probably a risk-benefit analysis:

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• it's a small effect compared to the big-picture basics, like carrying speed out of a corner, that everyone must learn early on

• it's difficult to learn, so why burden new students with it?

• mistakes with it are ugly

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Another reason may have been that my instructors hadn't got their butts kicked recently by a trail-braking driver. It was not a commonplace technique back then, so one might drive a whole season of club racing without getting spanked by trail braking. Since not everyone used it, not everyone had to develop the skill. Nowadays, however, the general level of driving skill has increased to the point where it's no longer optional, unless you're content with fourth place. As with most driving skills, it's difficult to get a feel for the limits without exceeding them from time to time. However, exceeding the limits at trail braking has some of the worst consequences one can invite on a race track, typically worse than those from mistakes at corner exit. It's definitely a big risk for a small effect, justified only because it accumulates. Blowing it results in too high an entry speed. You get:

• inappropriate angular attitude in the corner

• immediate probing of the understeer or oversteer characteristics of the car

• surprise, pop quiz on the driver's car-control skills

• missed apex and track-out points

• a looming penalty cone, gravel trap, tyre barrier, concrete wall, tree, etc.

• when you bounce back from that impact, you can hit other cars, spectators, corner marshals, berms, etc.

• anything else that can go wrong in a blown corner

That's one of the reasons I have not, in the past, singled it out for my personal driverdevelopment work - it's hard to do at all and harder to do it consistently and just didn't seem worth it. Another reason is that the kinds of cars I like to drive let you get away without it much of the time. I prefer ultra-powerful cars because they're fun and loud and attract a lot of attention. Paradoxically, though, such cars can lull one into becoming a lazy driver. With a lot of power on tap, you can often make up for an overly conservative entry speed on the exit.

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However, when the cars are equalized, as in spec races, showroom stock, or in a lot of Solo II car classes, trail braking takes a prominent role. It can be difficult to spot it as an issue in Solo II, where drivers are alone against the clock. All else being equal, a Solo II driver without trail braking may just find himself scratching his head wondering how in blazes the other drivers can be so much faster. Go wheel-to-wheel on the track with equal cars, though, and the issue becomes instantly and visually obvious. You may be just as fast in the corner, coming out of the corner, down the straight. You may have perfect threshold braking. You may have perfect turn-in, apex and track out points. But that little extra later braking and entry speed will allow the trail-braker to take away several feet every corner. Corner after corner, lap after lap, he will gobble you up. I recently completed a road-racing school at Sebring International Raceway where this is precisely what I saw. In identical Panoz school cars, the drivers who were faster than I were doing it right there and nowhere else. My ingrained, outdated style did me in, and even though I had much, much more on-track experience than the rest of the students, and even though they weren't faster in top speed than I, and even though their cornering technique was not nearly as polished as mine, three (out of twelve) of them had better lap times than I. The instructors were

The instructors were as surprised as I. One even said he would have bet money that I was the quickest from watching me and riding with me (instructors did not ride in the wheel-to-wheel sessions). The clock doesn't lie though, and we were scratching our heads and I started swapping cars. Once we went wheel-to-wheel on the third day of the program, I spotted it, right there the first time into turn 2: the three quicker drivers took a car length from me on the corner entry. They did it again in turn 10 (Cunningham), at the Tower turn, and turn 15 approaching the back stretch: all the turns requiring full braking and downshifts. I made up a bit at the hairpin, which is an autocrosser's corner if there ever was one, and I knew the importance of not missing the apex by more than an inch or two if possible. They also couldn't beat me entering turn 17, which has no straight braking zone: instead, the best technique is to brake partially after turn in (at 115 mph, this is big-time, serious fun). Thus, turn 17 did not trigger my old-fashioned "braking-zone" program, and I was able to use my high-speed experience to coax a bit more than average grip through it. So, in sum, my conservative turn-ins on the slow corners added up to about half a second per lap, which is about 65 feet at the start-finish line where we're going about 90 mph =132 fps (90 x 22 / 15). Ugly. I was doing it the old-fashioned way: get the braking done in the bra

I was doing it the old-fashioned way: get the braking done in the braking zone and get your foot back on the gas pedal and up to neutral throttle before turn-in. That little tenth of a second or so where I'm coasting and they're still braking is the car-length they were taking out on me. It was small enough that the instructors couldn't feel it or see it. But electronic instrumentation would have picked it up. When I go back to the Panoz Sebring school next year, I will take advanced sessions in fully instrumented cars, where the instructors go out for some laps at 10/10s, then the students go out in the same car and take data. Back in the pits, the charts are differenced and the student can see precisely what he needs to do to come up to the instructor's level (most of the instructors have years of experience on the track, and hold current or former lap records in various cars on the course, so it's quite unlikely that a student will be as quick out of the box).

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The following is a picture of the course snipped from the web site at http://www.sebringraceway.com, so you can see the bits of the course I'm talking about:

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Let me say a few things about the school. The three-day program consisted of

• solo exercises in braking, skid recovery, and autocrossing

• detailed in-car instruction as driver and passenger over several lapping sessions

• racecraft including passing and rolling starts

• wheel-to-wheel sessions on the full open course

Sebring is large, exciting, lovely, complex course with a deep history of sports-car racing. It is currently 3.70 miles in length, though it has been as long as 5.7 miles in its history. Let's do some dead reckoning, that is, math in our heads without even envelopes to write on. We'll see if we can cook up some data, from memory, to justify the intuitions and explain the results above.

(advanced calculations)

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There are 2.54 centimetres per inch: that's an exact number. Therefore, there are 2.54 x 12 = 30.48 centimetres per foot. The number of centimetres per mile, then are 30.48 x 5280 = 30 x 52 x 100 + 30 x 80 + 48 x 52 + 48 x 80 / 100 = 156000 + 2400 + (50 - 2)(50 + 2) + 3840 / 100 = 158400 + 2500 - 4 + 38.40 = 160,934.4. Thus, a mile contains 1.609344 kilometres, which we can round to 1.61, which is, conveniently, 8/5 + 1/100. So 3.70 miles is 29.637 / 5 = 5.927 kilometres or just about 6. Now, there are 5280 / 3 = 1760 yards in a mile, so we have 3700 + 2590 + 222 = 6,512 yards, which is consistent with 6 kilometres, so we've got a check on our math. In fact, we can be a little more sanguine about it. Another number we remember is that there are about 39 inches per metre; that's a yard and three inches, or 13/12 yard. So, if we have about 6,000 metres, that's going to be about 6,000 + 6,000 / 12 = 6,500 yards. Amazing, isn't it? Finally, this is 6,512 x 3 = 13,036 + 6,512 = 19,048 feet.

A record time around the course in the Panoz school cars is 2 min 28 seconds. The students were doing 2:40 to 2:45. I believe I uncorked a 2:36 somewhere along the way, but my typical lap was 2:40 and the quicker guys pulled about 65 feet on me at the startfinish every lap, which I reckoned before to be worth half a second. What's the average speed at 2:40? That's 3.70 miles in 160 seconds. The average speed is 19,048 / 160 fps ~ 1905 / 16 ~ 476 / 4 ~ 119 fps, which is 119 x 15 / 22 mph, and that is (1190 + 595 ~ 1785) / 22 = 892.5 / 11. It's hard to divide by 11, so lets multiply instead. 80 mph by 11 would be 880, and that's not enough by 12.5. So, if we go with 81 mph by 11, namely 891, we're short by 1.5. A tenth of 11 will take care of some of that, so 81.1 by 11, namely 892.1, leaves us close enough. Now, doing the same distance in 2:28, or 148 seconds, yields an average speed of 19,048 / 148 ~ 4,762 / 37. Another tough divisor. Let's try 130 x 37 = 3700 + 1110 = 4810, too much by 48. But, we lucked out, it's obvious that 48 is about 1.30 x 37, so we get 130 - 1.30 = 128.7 fps. Now multiply that by 15 / 22: (1287 + 643.5) / 22 ~ 1930 / 22 = 965 / 11. 90 x 11 would be 990, too much by 25, which is a little more than 2 x 11. So 90 - 2 = 88 x 11 would be 880 + 88 = 968, too much by 3, so we'll reduce 88 by 0.3 x 11 to get 87.7. The average speed of a record-setting lap is 6.6 mph faster than our pitiful student laps! The difference is 12 seconds, so, as a rule of thumb, a second at 85 mph average is worth a little more than 1/2 an mph.

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But, before we wander too far off topic, let's compare 2:40 to 2:40.5, since my contention from the beginning of this note is THAT difference can be accounted entirely to trail braking in four corners of this course: 2, 10, 13, and 15. Well, at 119 fps, average speed, half a second is about 60 feet, which is about 4 car lengths. Yep, there you have it: one car length per significant corner due to trail braking. Darn it, looks like I'll just have to go back there and keep trying, over and over again.

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The End ->

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