How Can Changing Horsepower for Everyone Make Racing More Competitive?

I get this question a lot: If NASCAR decreases horsepower for everyone, how does that make it easier to pass? You’re basically taking everyone down by the same amount, right?

To explain this, we have to touch on a couple concepts.  Moody asked me this a couple weeks ago and I gave him a really crappy answer. I’ve been feeling guilty ever since.

Horsepower vs. Torque

We usually talk about horsepower when we talk about engines, but the important quantity here is actually torque. As a friend likes to say, horsepower lets you go fast, but torque makes you feel good.

Horsepower is how fast the engine delivers energy. (Power is energy divided by time.) Horsepower is actually a unit. It was proposed by James Watt (the 18th Century Scottish inventor, not the Secretary of the Interior under President Reagan). The Scottish Watt invented a viable steam engine by understanding some very complicated thermodynamics, most of which wouldn’t be formalized by scientists for another 100 years. His Watt Steam Engine was a critical driver of the Industrial Revolution.

Watt was successful at convincing a lot of people who ran factories to switch from the current Newcomen steam engine, which was extremely inefficient and used a lot of coal to make a little bit of power. Watt’s engine needed much less coal and he actually licensed the engine to people for royalties – he got 1/3 of the money they saved on coal relative to the Newcomen engine they had been using.

But there are only so many industries. Watt saw his engine as being useful to much smaller enterprises, like mills. But this was a different PR task. You weren’t convincing people to trade out one machine for another – you were convincing them to trade out their trusty horses — which work steadily and require only a little hay and water — for a machine.  It’s a real paradigm shift. How do you even compare two things that are so dissimilar?

Watt estimated – and I use the word ‘estimated’ loosely – the power of an average horse. He sort of measured it on what I’d describe as a horse dyno. That gave him a way to parameterize the power of his steam engine in terms of what he hoped to replace: the horse.

Nowadays, most of the world uses the metric unit for power – the Watt. One horsepower is 746 Watts. So that 60-Watt lightbulb in your lamp is actually a 0.08 horsepower lightbulb. A 1000-W hairdryer is about 1.3 hp. A 750-hp engine is the equivalent of 932 60-W lightbulbs.

Torque vs. Horsepower

Torque and horsepower are both properties of an engine. As we’ve discussed before, we usually talk about peak values (like the Mustang engine above is 300 hp at 6500 rpm), but the actual values depend on the engine speed (in rpm). A friend who designs engines likes to tell me…

Horsepower lets you go fast. Torque makes you feel good

Power is how fast you can supply energy – and determines your ultimate speed. But when you step on the gas, what you really want is acceleration.

A minivan and a Mustang both reach 60 mph. But there’s a big difference between punching the gas and hitting 60 mph at the end of the on-ramp and standing on the gas and it taking fifteen seconds to get to 60 mph. Speed is good, but acceleration is actually much more important. And acceleration requires torque.

Torque and horsepower are related, as shown in the graph below.

Every torque and hp curve you see will have the torque and the horsepower curves cross at the engine speed of 5252 rpm. That’s because the horsepower and the torque are related to each other by a pretty simple equation.

 

So when NASCAR limited horsepower, they also effectively limited torque. That, in turn, limits how much acceleration you get.

Kinematics and Quadratics

This is a perfect time of year to discuss this because every high school student starting a physics class is probably learning about distance, velocity and acceleration right now.

Velocity is how much distance you travel in a particular amount of time. If you’re going 60 mph, it literally means that you go 60 miles every hour.

Acceleration is how fast you change your speed. A Bugatti Veyron goes from 0 to 60 mph in 2.4 seconds, which means that it goes (on average) 25 mph more every second,.

When you’re coming out of turn 2 or turn 4, onto the straightaway, what you want is acceleration. You’ve had to slow down to take the corner, so the goal is to be going as fast as possible coming out of the turn, accelerate as quickly as possible, and put as much distance between you and the guy behind you as possible.

No Acceleration

The distance you travel at a constant speed is proportional to the time.  If you go 60 mph, after one hour, you’ve gone 60 miles. After two hours, you’ve gone 120 miles. After three hours, you’ve gone 180 miles. It’s linear.

This seems obvious, but if I am behind you by half a second, there’s no way I can pass you unless I go faster. But just look at how much faster I have to be going.

Car 1 is the blue line, going at 180 mph. Assume car 2 is a half second behind. If car 2 goes 190 mph, then it will take just about 9 seconds for car 2 to pass car 1and that’s the red line.

If Car 2 goes 200 mph, it takes only about 3 seconds for car 2 to pass car 1.

Of course, if we’re talking about cars directly battling for position, we’re probably talking about one being a tenth of a second behind. In that case, if car 1 goes 180 mph, car 2 going 182 mph would take almost six seconds to pass and car 2 going 184 mph would take about 2 seconds.

The Magic of Quadratic Dependence

Here’s the big deal for acceleration. The distance you travel is proportional to the SQUARE of the time.

Let’s do this first with simple math. Let’s say you accelerate such that you travel 100 feet in one second. After two second, you haven’t gone 200 feet – you’ve gone 400 feet. And the longer you go, the bigger the difference gets.

I think graphs are easier to see this, so here’s a representative graph. Both cars have the same acceleration; however, Car 2 doesn’t start accelerating until half a second AFTER Car 1.

The interesting thing here is that the distance between the two cars doesn’t stay the same. Car 1 gets further and further ahead just because how far it goes depends on the square of the time. Car 2 never catches Car 1.

Another words, the long Car 1 accelerates, the more distance it puts between it and the car behind it.

What if Car 2 can accelerate faster?

After some time, Car 2 will pass Car 1. How long that takes depends on both car’s accelerations.

But there’s one more important thing we have to consider.  How long the cars accelerate.

Terminal Speed

An engine can’t accelerate indefinitely. At some point, it reaches its top (or terminal) speed. Then the distance it travels goes back to depending linearly on time. The graph below shows a car that accelerates for four seconds, then reaches its terminal speed. Notice how the graph changes from being quadratic to being linear at the crossover?

 

Compare that graph with how far the car would’ve gone if it kept accelerating. I’ve shown the quadratic in blue below and the same behavior as in the graph above in red. You can see how much further the accelerating car goes and that distance just keeps growing bigger the longer you go out in time.

When you reduce engine power, you have a lower terminal speed and you reach it faster. That means you don’t get to put as much distance between you and the next guy. And that was the big complaint in a lot of places. One guy gets out front coming out of turn 2 or 4, gets a big lead coming down the straightaway, and the guys behind don’t have a chance of catching him.

At the big places like Indy and Michigan, that was one of the big problems. A car got going down the straightaway and it was gone. There was no catching up to it. The theory behind the lower horsepower there is that the cars reach terminal speed faster, which limits how much of a lead a car can get. The same idea applies pretty much anywhere.

So why doesn’t NASCAR just do the calculation and figure out the sweet spot for each track? Too many variables. A driver will get on the gas at a different point coming out of a turn, or brake later going in. There’s no way to precisely figure it out.

But the general principle applies. If you limit acceleration and top speed for everyone, you limit how much of a lead a car can get. That means that the cars behind have a chance at passing for the lead.