The Physics of Speed: A Tale of Tire Force and Friction

As we explore the world of high-performance vehicles, one question often arises: which car will be quicker to reach 60 miles per hour? The answer may seem straightforward, but it's actually influenced by a complex interplay of factors, including tire force and friction. To understand this phenomenon, let's dive into the world of physics.

A graph illustrating the relationship between vertical load and coefficient of friction is presented, highlighting how an increase in vertical load can overpower a decrease in coefficient, resulting in an increase in traction. This concept is crucial when considering the performance of different vehicles on the road. For instance, a 1000-pound car with a coefficient of friction of 1.45 is compared to a 5,000-pound car with a coefficient of friction of 1.1. The equation F = ma (force equals mass times acceleration) is used to calculate the maximum force that the tire can apply to the ground, which is equal to the coefficient of friction multiplied by the normal force.

Using this equation, we can determine the acceleration of each car. For the 1000-pound car with a coefficient of friction of 1.45, the calculation yields 1.45 Gs (g-forces), while the 5,000-pound car with a coefficient of friction of 1.1 results in an acceleration of 1.1 Gs. This correlation between coefficient of friction and acceleration highlights how critical tire force is to achieving high speeds.

Now, let's consider how the weight of a vehicle affects its acceleration. Using the same equation, we can calculate the acceleration of both cars with infinite power and the same tires and coefficient of friction. The result shows that despite having more power, the heavier car (5,000 pounds) accelerates less than the lighter car (1000 pounds). This is because the force required to accelerate a heavier vehicle is greater, but the tire force also decreases as a result of lower traction.

This phenomenon can be attributed to tire load sensitivity, which explains why adding mass to a system like this doesn't necessarily lead to increased acceleration. However, there are scenarios where adding mass can improve acceleration, such as in two-wheel drive setups. For those interested in learning more about tire load sensitivity and its effects on vehicle performance, I highly recommend checking out Carol Smith's book.

In conclusion, the relationship between tire force and friction plays a significant role in determining a vehicle's acceleration. Understanding this complex interplay is essential for anyone looking to optimize their vehicle's performance or simply appreciate the physics behind high-speed vehicles. Whether you're a car enthusiast or just someone curious about the world of speed, I hope this article has provided valuable insights into the fascinating realm of tire force and friction.

A link to Carol Smith's book is included in the video description for those interested in exploring this topic further. If you have any questions or comments regarding the physics of speed or tire force and friction, feel free to leave them below.

"WEBVTTKind: captionsLanguage: enHello, everyone and welcome in this videoWe're going to be talking about how Tesla hit 60 miles per hour in just 2.28 seconds. Now this video was inspiredActually by a reddit threadyou know someone posted that Motor Trend had tested out the new Tesla P100Dand they broke their record; the first car they've ever tested getting under 2.3 seconds 0 to 60 timeBut then there was a lot of discussion of what if we put this package into a Tesla RoadsterWould it be faster or would it be slower because the Roadster weighs less?And so there was a lot of confusion in this discussion threadabout grip so in order to get a really fast 0 to 60 time you really need three things. You need a ton of powerThe Tesla P100D has680 horsepower so it's got plenty of power. You need all-wheel drive so that you can put all of that power to the ground.Model S P100D has all-wheel drive.and you need grip and grip is the one that confuses people and so that's what we're going to kind of get into hereNow if you've watched my video on what is the fastest 0 to 60 time possible you'll recall that the logicI use is looking at the braking distance of vehicles in order to determinewhat's the fastest 0 to 60 time possible using street tires.Not race tires, street-legal tires and so using that logic. You look at the braking of a vehicle because that's using itsMaximum amount of grip possible the ABS Motors kick in if there is slip in order to allow it to rotateFurther and not just slide until you're going to be hitting the edge of the grip of those tiresAnd you're going to be decelerating as fast as possibleSo the reverse logic is, if you can decelerate that fast if you have enough powerWhich this car does it's got plenty of horsepower, then you can accelerate at that same rateAnd so that grip limit as discussed in that video if you want the derivation from these equations. You might want to check that outbut distance equals one-half velocity squared divided by accelerationthe distance that MotorTrend was able to stop with the P85D was102 feet the P100D they stopped in a hundred nine feetBut I'm going to go with this one because it's the most extreme and it's the theoretical limit of this Tesla Model Sthat's the best they've ever had and this is also the bestAcceleration test they've ever had so I'm going to compare those two to each otherSo 102, oh and you're going to be angry about units I already know thatApologies these are units straight from MotorTrendMaybe write them a letter and tell them to switch their magazine to metric units if you don't like thatAnyways these are the units that they use, so I'm going to continue to use them 102 equals one-half 88 squared88 is feet per second, that's 60 miles per hour converted to feet per second. So 88 feet per second equals 60 miles per hourDivided by AWe solve for A, A gives us37.9 feet (feet) per second squared .96 feet per second squared, so this number if you divide that by32.2 that's the acceleration of Gravity on Planet Earth that gives you 1.18 gso this car is able to decelerate based on a stopping distance of 102 feet at1.18 G's so I would assume it would also be able to accelerate if it had enough power based on the grip of the tiresso velocity equals acceleration times time we take 88 feet per second divide that by37.96and that gives us a 0 to 60 of 2.32 seconds2.32 seconds as you will notice is very close to Motor Trend's 2.28 secondsSo I'm saying theoretical limit based on braking is 2.32. They actually beat that with a 2.28Regardless, they are very closeBut there are a couple things to keep in mind about why this number could theoretically be better than this numberFirst of all the Model S P100D has larger rear tires, so when you have load transfer those rear tiresThey will have more grip versus when you're braking you have skinnier tires up front which are handling more loadAnd that's going to be one small difference, now it's a small differenceI think it's only 20 millimeters wider in the rear but once again. This is a very small difference as well 2.28 vs 2.32The other thing to keep in mind. Is th at it has a51/49 Weight distribution according to MotorTrend the vehicle they tested, so that means more weight in the frontSo what this means is when you're braking you're going to have relatively more load on the front tiresThan when you're accelerating because that center of gravity is closer to those front tiresSo under braking the front tire has more load than the rear tireRelatively more speaking then how much the rear tire has under accelerating versus the front tireWhat that means is the weight distribution is more even under accelerationThan it is under braking and a more even weight distribution under accelerationmeans you'll have slightly more traction in order to accelerate faster, and that can help explain how they got 2.28 vs 2.32Ok so that's how Tesla did it, really it's just power, grip and all-wheel-drivebut all of the confusion came from this question right hereIn this reddit thread where they said you know what if they put this package in a Tesla RoadsterHow quick would that thing be would it actually be faster, and they were two kind of conflicting arguments hereSome people would say yes, it's lighter thereforeIt would be quickerAnd then other people would say no because the Model S has more weight it has more tractionAnd so I think a lot of that confusion comes from this book Carol Smith's 'Tuned to win'Which is actually a fantastic bookAnd within it there are two graphs which are actually pretty helpful to look at the first one coefficient of frictionVersus vertical Tire load, and you can see that as the tire load on a vehicleincreases the coefficient of friction of that tire with the grounddecreases so what this is saying is that as you increase weight you're decreasing the amount of grip that, that tire hashoweverThere is also a graph in this book that shows that as you increaseVertical load on the tire the amount of force that the tire can apply to the ground increasesSo traction is increasing with an increase in vertical loadNow the sentence that Smith says in this book which I think confuses a lot of people as he says the curve is so gentlethat the increase in vertical loadOverpowers the Decrease in coefficient, and so if you're looking at this graph here the vertical load increasesand the amount of traction that the tire has increases even though your coefficient of Friction is going down, soApplying that to our question here would a roadster be quickerwellThere's some very simple math which we can do in order to prove(which) if it's yesor no to that question so looking at his exact chart and just pulling some data points from it if we look ata 1000 pound car we can read that it has a coefficient of friction with just 250 pounds per tire of1.45 if we look at a 5,000 pound car we can see that it has 1,250 pounds per tire for coefficient of friction of1.1 now if we look at the equation for the maximum Force that the tire can apply to the ground that's going to be equalto the coefficient of frictionmultiplied by the normal Force in this case 1.45 times 1000 this will give us1,450 pounds Forcethat's the maximum force assuming the car has enough horsepower for it that it can be applied to the ground without the tire spinningSo F equals ma1450 Divided by1000 pounds mass, we're just calculating the acceleration here so A equals F divided by M. There's our forceThere's our mass that gives us1.45 G's if we do the same for our 5,000 pound car assumingIt has plenty of Horsepower and can take care of that end of it. We're going to do 5,000 times 1.1That's going to give us 5,500 pounds force5,500 pounds Force 5,000 pounds mass is going to give us1.1 Gs. You'll notice this correlates perfectly with the coefficient of frictionso how fast will you get to 60 using an acceleration of1.45 Gs, you take 88 you divide that by 1.45 times32.2 that's Gravity in feet per second squared on planet Earth at sea level and that is going to give us1.88 seconds you do the same for1.1 Gs and that's going to give you2.48 Gs Oh 2.48 seconds, sorryAnd so you can see there's a point six difference here in timePurely from weight so both of these cars have infinite power the only thing holding them back is gripAnd you can see that because this car weighs4,000 pounds less its coefficient of Friction is higher and therefore it is able to accelerate fasterSo yes a Tesla Roadster fitted with a P100DAssuming it could keep its weight less than the P100D Model S would be faster to 60Because the coefficient of Friction would be lowerSomething that this graph here doesn't show you is that acceleration would be constantit would just be a linear line coming out like that, not a very linear line, but you get the ideait would just be a straight line coming out and because of this coefficient of Friction is decreasingThat tire Force is decreasing as wellAnd so normally if both of these cars had the exact same tires and the exact same coefficient of frictionAnd the same and infinite power, they were both accelerate at the exact same rateso you know the equation here really just comes from F equals maSo acceleration equals Force divided by MassAs you increase mass the force does not increase as much so that would be this line here, but insteadIt's less the Tire Force is lessAnd so you're having an equation or this number is getting slightly smaller relative to this number which means your acceleration is getting smallerSo you cannot add MassTo a system like this and have it accelerate faster there are scenarios in which adding MassCan increase how quickly you accelerate but that tends to be with two-wheel drive setups and I do have a video explaining thatnow I think a big part of the confusion of all of this is something called Tire load sensitivityAnd it's one of my much less viewed videos that I would highly recommend checking outpurely because it helps explain why this coefficient of friction drops and why heavier cars are going to have aLess traction and be able to accelerate more slowly it also explains why wider tires give you more gripalso I will include a link in the video description to Carol Smith's book if you're interested in this kind of stuffIt's a fantastic book for learning more about this material. So thank you guys for watchingThank you to whoever you know pulled me in on the comment thread there on redditAnd if you guys have any questions, or comments feel free to leave them below\n"