Fx: The Bugatti Chiron has just under 1500hp and a top speed of MAX 500kmh, while a Volkswagen Golf has 150hp and a top speed of around 200kmh.
In: Physics
Drag scales with speed squared. Twice the speed = four times the power required.
So 10x the horsepower gives you square root of 10 = ~3.2 the speed.
Horsepower is exactly that.
If you have 1 horse pulling a carriage or two horses pulling a carriage, do you expect to go a lot faster?
With more horses it is more power, which creates slightly more speed, but only because there are more horses.
Each individual horse can only run so fast, more horses simply means they can run closer to the speed they would if they weren’t pulling anything 🙂
Air resistance (as Tdscanuck nicely described) but also other factors such as power to weight ratios.
The level of engineering & engine size between these vehicles is vast.
A Bugatti with a W16 engine weighs in at 1996kg with a top speed of 490km/h = 0.24 km/kg
A Vw golf gti 4 cylinder weighs 1415kg with a top speed of 250km/h = 0.18 km/kg
Power requirements don’t scale linearly with speed, they scale with the *cube* of speed which means that in a given car, traveling at 400kph requires 8x the power as traveling at 200 kph.
At high speeds the air resistance is what limits the car’s speed, the force from the air resistance scales with the speed squared (F_drag=0.5 * density * Velocity^2 * Drag Coefficient * Area). But power is work over time, and work is force times distance which means the power also scales with the speed so the end result is that the power needed goes up by the cube so you need *at least* 8x the power to double the speed because we’ve completely ignored other non-ideal effects like rolling resistance.
There are a lot of forces (namely friction and air resistance) that work to actively stop a car from speeding up past a certain point.
This all comes down to energy being proportional to mass but also to velocity squared; as you go faster, the harder the air is hitting you and pushing back, and it goes up exponentially as you keep speeding up. Similarly, all of the moving parts heat up exponentially more from friction as you increase the speed they rub against each other.
Because of that, you end up needing an exponential increase in power to maintain linear gains in speed.
Allow me to introduce you to what is known as the law of diminishing returns.
Let’s say you want to learn to do something, like play guitar. You learn the basic major chord shapes, learn how to play them in a basic 4/4 count. You can play guitar…but you’re not that great, rather basic and vanilla. This is because you’ve only spent a brief amount of time doing it. If you spend more time, you’ll get soooooo much better, right?
No. Once the basics have been taken aboard, from there the learning curve tends to level off. You stop making huge jumps in knowledge and everything gets a little harder. You picked up 12 major and minor chords with ease in an hour…but from there things slowed down. To get into augmented chords and understand how they work might’ve taken twenty hours or more. It takes 10% of the time to learn 90% of the stuff, but that last 10% of stuff will take the rest of your life to acquire.
The speed of the cars is much the same. Getting a car to 200kmh isn’t *easy* but it’s easy enough that most automakers can do it with relative ease. That’s learning Emajor, Amajor, Bmajor, and how to play them in a basic 4/4 count.
Getting to 500kmh? That’s learning how to sight-read music in different keys while playing two separate compositions at the same time. MUCH more work, much more effort, much more force necessary. The guy everybody knows who has a guitar in the closet is a product of 90% of the material learned. Tommy Emmanuel is a product of striving for a lifetime to get the last 10%.
Getting science-y on it, every car on every road is fighting the air in front of it to move. The faster you try to move, the more air the car has to push out of the way. Think of it like running in water; moving slowly is easy, but every bit faster you try to go, the more work it becomes. At 200, there’s a lot of air being displaced, but at 500 you’re displacing twice as much and half again, 250% more air that has to be bullied out of the way every millisecond. At some speed, the car will be trying to force the air volume of a mountain out of the way every second just to hold that speed steadily. To gain even 1 measly kmh means adding another mountain’s worth of air mass that has to be moved aside!
Moving that much more air out of the way, it takes power. It takes 10X to get 250% faster, but to go 250% faster than that would probably take 50X as much power. 1250kmh might take 75000 horsepower. Every little bit of speed increased is way more work and way more effort. At a speed like 500kmh, at some point that car could be pushing several metric tons of air out of the way every second. Increase the speed to 550 and it’s pushing twice as much air it’s trying to displace.
This isn’t even considering friction of the mechanisms, etc. Propulsion is difficult and very expensive. There’s a reason to launch even a small rocket to orbit it needs tons and tons and tons of fuel. If you can throw a ball at 150kmh at maximum exertion, how much work is it for you to throw the ball at 175kmh? It’s only a difference of 25kmh, a wimpy 14% increase, but the amount of work to throw it 14% harder may be beyond your capability.
Little increases tend to get more “expensive” as progress is made. To make the Chiron hit 600, horsepower would have to increase hugely, and the going fast isn’t cheap; it’d not only be the fastest by far, but the most expensive by far!
Helping you (hopefully), Intuit the square cube law.
Imagine walking through a sparsely populated field, every so often you need to move left or right to dodge a rock, tree or have to push a branch out of the way. While you’re walking you perform these actions 10 times a minute.
You decide you need some extra exercise so you’re going to run – now every minute you’re covering more ground and you’re dodging more, swatting more and paying more attention, thinking faster.
This higher pace allows you to cover more ground faster but because of the extra cognitive load and increased rate at which you’re dodging or pushing things out of your way you’re using more energy every minute and you’re no longer getting a break it’s relentless, one thing after another.
This feeling of many things getting harder at once as you go a bit faster is the square cube law – as you go faster you’re not just linearly expending energy overcoming inertia you’re also fighting air resistance moving through a given amount of air particles takes at least a given amout of energy and if you want to do it in less time you need more energy per second in addition to more energy per second to continue overcoming interia.
Latest Answers