Our speedometers go to 200 MPH - who's been there ?

[Ngilbe36]

This thread is almost annoying me enough to do some actual calculations for aerodynamics and flow as well as see if the gearing in these cars could actually get you there. That would probably just break the internet to provide actual facts and data so I will hold off.

[carenthuziast]

Originally Posted by Merlin_83

Greetings,

Ok - we ll know our M3's are very capable of double digits . Who has (on a closed course, race track) reached burying that speedo needle..all the way to the 5 o'clock position and got the V8 S65 to 200 MPH ?

(disclaimer) I only would recommend people test their cars at a closed course or dedicated race course to conduct any kind of high speed test..

Ok, that being stated - who's got pictures and proof of the illustrious 200 MPH...????



Cheers,
Merlin

Should this question even be asked?

All those who have attempted 200 mph are now deceased. Others who say they have done it are lying.

[DSilk]

Originally Posted by Ngilbe36

This thread is almost annoying me enough to do some actual calculations for aerodynamics and flow as well as see if the gearing in these cars could actually get you there. That would probably just break the internet to provide actual facts and data so I will hold off.

Be my guest:

The Physics of Racing,
Part 6: Speed and Horsepower
Brian Beckman

physicist and member of
No Bucks Racing Club

P.O. Box 662
Burbank, CA 91503

©Copyright 1991
The title of this month's article consists of two words dear to every racer's heart. This month, we do some "back of the envelope" calculations to investigate the basic physics of speed and horsepower (the "back of the envelope" style of calculating was covered in part 3 of this series).

How much horsepower does it take to go a certain speed? At first blush, a physicist might be tempted to say "none," because he or she remembers Newton's first law, by which an object moving at a constant speed in a straight line continues so moving forever, even to the end of the Universe, unless acted on by an external force. Everyone knows, however, that it is necessary to keep your foot on the gas to keep a car moving at a constant speed. Keeping your foot on the gas means that you are making the engine apply a backward force to the ground, which applies a reaction force forward on the car, to keep the car moving. In fact, we know a few numbers from our car's shop manual. A late model Corvette, for example, has a top speed of about 150 miles per hour and about 240 hp. This means that if you keep your foot all the way down, using up all 240 hp, you can eventually go 150 mph. It takes a while to get there. In this car, you can get to 60 mph in about 6 seconds (if you don't spin the drive wheels), to 100 mph in about 15 seconds, and 150 in about a minute.

All this seems to contradict Newton's first law. What is going on? An automobile moving at constant speed in a straight line on level ground is, in fact, acted on by a number of external forces that tend to slow it down. Without these forces, the car would coast forever as guaranteed by Newton's first law. You must counteract these forces with the engine, which indirectly creates a reaction force that keeps the car going. When the car is going at a constant speed, the net force on the car, that is, the speeding-up forces minus the slowing-down forces, is zero.

The most important external, slowing-down force is air resistance or drag. The second most important force is friction between the tyres and the ground, the so-called rolling resistance. Both these forces are called resistance because they always act to oppose the forward motion of the car in whatever direction it is going. Another physical effect that slows a car down is internal friction in the drive train and wheel bearings. Acting internally, these forces cannot slow the car. However, they push backwards on the tyres, which push forward on the ground, which pushes back by Newton's third law, slowing the car down. The internal friction forces are opposed by external reaction forces, which act as slight braking forces, slowing the car. So, Newton and the Universe are safe; everything is working as it should.

How big are the resistance forces, and what role does horsepower play? The physics of air resistance is very complex and an area of vigorous research today. Most of this research is done by the aerospace industry, which is technologically very closely related to the automobile industry, especially when it comes to racing. We'll slog through some arithmetic here to come up with a table that shows how much horsepower it takes to sustain speed. Those who don't have the stomach to go through the math can skim the next few paragraphs.

We cannot derive equations for air resistance here. We'll just look them up. My source is Fluid Mechanics, by L. D. Landau and E. M. Lifshitz, two eminent Russian physicists. They give the following approximate formula:



The factors in this equation are the following:

Cd = coefficient of friction, a factor depending on the shape of a car and determined by experiment; for a late model Corvette it is about 0.30;
A = frontal area of the car; for a Corvette, it is about 20 square feet;
= Greek letter rho, density of air, which we calculate below;
v = speed of the car.
Let us calculate the density of air using "back of the envelope" methods. We know that air is about 79% Nitrogen and 21% Oxygen. We can look up the fact that Nitrogen has a molecular weight of about 28 and Oxygen has a molecular weight of about 32. What is molecular weight? It is the mass (not the weight, despite the name) of 22.4 litres of gas. It is a number of historical convention, just like feet and inches, and doesn't have any real science behind it. So, we figure that air has an average molecular weight of



I admit to using a calculator to do this calculation, against the spirit of the "back of the envelope" style. So sue me.

We need to convert 1.29 gm/l to pounds of mass per cubic foot so that we can do the force calculations in familiar, if not convenient, units. It is worthwhile to note, as an aside, that a great deal of the difficulty of doing calculations in the physics of racing has to do with the traditional units of feet, miles, and pounds we use. The metric system makes all such calculations vastly simpler. Napoleon Bonaparte wanted to convert the world the metric system (mostly so his own soldiers could do artillery calculations quickly in their heads) but it is still not in common use in America nearly 200 years later!

Again, we look up the conversion factors. My source is Engineering Formulas by Kurt Gieck, but they can be looked up in almost any encyclopaedia or dictionary. There are 1000 litres in a cubic meter, which in turn contains 35.51 cubic feet. Also, a pound-mass contains 453.6 grams. These figures give us, for the density of air



This says that a cubic foot of air weighs 8 hundredths of a pound, and so it does! Air is much more massive than it seems, until you are moving quickly through it, that is.

Let's finish off our equation for air resistance. We want to fill in all the numbers except for speed, v, using the Corvette as an example car so that we can calculate the force of air resistance for a variety of speeds. We get



We want, at the end, to have v in miles per hour, but we need v in feet per seconds for the calculations to come out right. We recall that there are 22 feet per second for every 15 miles per hour, giving us



Now (this gets confusing, and it wouldn't be if we were using the metric system), a pound mass is a phoney unit. A lb-mass is concocted to have a weight of 1 pound under the action of the Earth's gravity. Pounds are a unit of force or weight, not of mass. We want our force of air resistance in pounds of force, so we have to divide lb-mass ft / sec2 by 32.1, numerically equal to the acceleration of Earth's gravity in ft / sec2, to get pounds of force. You just have to know these things. This was a lot of work, but it's over now. We finally get



Let's calculate a few numbers. The following table gives the force of air resistance for a number of interesting speeds:

v (mph) 15 30 60 90 120 150
F (pounds) 3.60 14.5 58.0 130 232 362

We can see that the force of air resistance goes up rapidly with speed, until we need over 350 pounds of constant force just to overcome drag at 150 miles per hour. We can now show where horsepower comes in.

Horsepower is a measure of power, which is a technical term in physics. It measures the amount of work that a force does as it acts over time. Work is another technical term in physics. It measures the actual effect of a force in moving an object over a distance. If we move an object one foot by applying a force of one pound, we are said to be doing one foot-pound of work. If it takes us one second to move the object, we have exerted one foot-pound per second of power. A horsepower is 550 foot-pounds per second. It is another one of those historical units that Napoleon hated and that has no reasonable origin in science.

We can expend one horsepower by exerting 550 pounds of force to move an object 1 foot in 1 second, or by exerting 1 pound of force to move an object 550 feet in 1 second, or by exerting 1 pound of force to move an object 1 foot in 0.001818 seconds, and so on. All these actions take the same amount of power. Incidentally, a horsepower happens to be equal also to 745 watts. So, if you burn about 8 light bulbs in your house, someone somewhere is expending at least one horsepower (and probably more like four or five) in electrical forces to keep all that going for you, and you pay for the service at the end of the month!.

All this means that to find out how much horsepower it takes to overcome air resistance at any speed, we need to multiply the force of air resistance by speed (in feet per second, converted from miles per hour), and divide by 550, to convert foot-lb/sec to horsepower. The formula is



and we get the following numbers from the formula for a few interesting speeds.

v (mph) 30 55 65 90 120 150 200
F (pounds) 14.5 48.7 68.0 130 232 362 644
horsepower 1.16 7.14 11.8 31.3 74.2 145 344

I put 55 mph and 65 mph in this table to show why some people think that the 55 mph national speed limit saves gasoline. It only requires about 7 hp to overcome drag at 55 mph, while it requires almost 12 hp to overcome drag at 65. Fuel consumption is approximately proportional to horsepower expended.

More interesting to the racer is the fact that it takes 145 hp to overcome drag at 150 mph. We know that our Corvette example car has about 240 hp, so about 95 hp must be going into overcoming rolling resistance and the slight braking forces arising from internal friction in the drive train and wheel bearings. Race cars capable of going 200 mph usually have at least 650 hp, about 350 of which goes into overcoming air resistance. It is probably possible to go 200 mph with a car in the 450-500 hp range, but such a car would have very good aerodynamics; expensive, low-friction internal parts; and low rolling resistance tyres, which are designed to have the smallest possible contact patch like high performance bicycle tyres, and are therefore not good for handling.

[Ngilbe36]

Originally Posted by DSilk

Be my guest:

The Physics of Racing,
Part 6: Speed and Horsepower....

For the record, I agree with you that this car cannot reach 200mph stock and yes, I know the contributing factors. I am a mechanical engineer working in the automotive field (not a brag or plug, just context).

[Richbot]

A 6mt can’t reach 200 because 6th gear tops pit at 196 at 8400 rpm on stock tires...even if ou add 1” for tire growth (well beyond the range of plausibility) you still only get to 204. 8400 is past the power peak and the car likely won’t let you have 8400 rpm in 6th gear because it takes some revs away as it heats up on the way up there. Most dynos show soft limiter kicking in around 8250. That’s 193 on the stock tires.

A dct can’t reach 200mph because 6th tops out just over 170 and 7th is too tall to drag as far as the 6mt top gear will take you.

No aero calcs necessary

But there’s plenty of documentation of these cars north of 180mph in stockish form. And bmw limited them to 178 in Europe with a de limit option. So 300kph is perfectly plausible in the real world.

[carenthuziast]

Originally Posted by Richbot

A 6mt can’t reach 200 because 6th gear tops pit at 196 at 8400 rpm on stock tires...even if ou add 1” for tire growth (well beyond the range of plausibility) you still only get to 204. 8400 is past the power peak and the car likely won’t let you have 8400 rpm in 6th gear because it takes some revs away as it heats up on the way up there. Most dynos show soft limiter kicking in around 8250. That’s 193 on the stock tires.

A dct can’t reach 200mph because 6th tops out just under 180 and 7th is too tall to drag muchh further

No aero calcs necessary

Many hearts are broken that you're saying a 6MT is actually faster than the DCT.

[Richbot]

Heh

You’ll be about a football field behind by the time the dct shifts into 7th, but you’ll catch up just keep going

[carenthuziast]

Originally Posted by Richbot

Heh

You’ll be about a football field behind by the time the dct shifts into 7th, but you’ll catch up just keep going

quite the overestimation in distance apart, but still faster bro...top speed

[Richbot]

The way most people drive I don’t think it’s an overestimate. Most people who drive stick because save the manuals still can’t drive worth a damn and those who can wouldn’t be in this theoretical race to begin with

[Ngilbe36]

Originally Posted by Richbot

The way most people drive I don’t think it’s an overestimate. Most people who drive stick because save the manuals still can’t drive worth a damn and those who can wouldn’t be in this theoretical race to begin with

I've got over 10,000 miles on my 6MT and would eagerly admit that I have not mastered it yet. "can't drive worth a damn" might be overstating it.

[carenthuziast]

Originally Posted by Ngilbe36

I've got over 10,000 miles on my 6MT and would eagerly admit that I have not mastered it yet. "can't drive worth a damn" might be overstating it.

..which makes the 6MT so fun because it's a challenge.

[dparm]

Originally Posted by Gears_and_Gasoline

I can tell you from my personal experience that the e90 m3 is very stable with the needle burried. (whether that's 200mph or not). Car had kw clubsport 3 ways, te37sl, 295/275 18's. Full interior with 2 occupants.

You've got several advantages over a stock sedan: stiffer suspension (probably lower, too), more rubber on the road, more weight in the car to help hold it down.

[PINHEAD]

they hit 200mph in their e92 because they're just better than you and have bigger balls

[Merlin_83]

Originally Posted by carenthuziast

quite the overestimation in distance apart, but still faster bro...top speed

Whoa...the 6 MT is faster after all

[roastbeef]

Originally Posted by carenthuziast

quite the overestimation in distance apart, but still faster bro...top speed

Probably not verts tho.

[///M Power-Belgium]

Originally Posted by DSilk

The BMW installed speed limiter kicks in at 155 mph. That is not what prevents the M3 from hanging with the F430 in top speed. What keeps the M3 from staying with the Ferrari is greater total aerodynamic drag coupled with less power. It's as simple as that. Superman may be able to fly on the big screen, but in real life the laws of physics get in the way.

*Superman* is the keyword in your statement .

[///M Power-Belgium]

Originally Posted by PINHEAD

they hit 200mph in their e92 because they're just better than you and have bigger balls

Let us say....Been born with big balls .
Note : This can cause serious issues with giving birth .

[spazzyfry123]

Originally Posted by roastbeef

Have you played the new one? It's ok, not as addicting as the old ones, but I have a ton of fun with the livery editor. Made some of my old favorites, and adopted the 90's oreca theme to a mustang.

Damn you're not half bad with that stuff. I ditched the Playstation a while back for the X-Box. I've been a Forza nerd for a while now. I actually think the last Gran Turismo I played is THE one back in the day (2...?)

[Green-Eggs]

Originally Posted by Ngilbe36

This thread is almost annoying me enough to do some actual calculations for aerodynamics and flow as well as see if the gearing in these cars could actually get you there. That would probably just break the internet to provide actual facts and data so I will hold off.

Originally Posted by DSilk

Be my guest:

The Physics of Racing,
Part 6: Speed and Horsepower
Brian Beckman

physicist and member of
No Bucks Racing Club

P.O. Box 662
Burbank, CA 91503

©Copyright 1991
The title of this month's article consists of two words dear to every racer's heart. This month, we do some "back of the envelope" calculations to investigate the basic physics of speed and horsepower (the "back of the envelope" style of calculating was covered in part 3 of this series).

How much horsepower does it take to go a certain speed? At first blush, a physicist might be tempted to say "none," because he or she remembers Newton's first law, by which an object moving at a constant speed in a straight line continues so moving forever, even to the end of the Universe, unless acted on by an external force. Everyone knows, however, that it is necessary to keep your foot on the gas to keep a car moving at a constant speed. Keeping your foot on the gas means that you are making the engine apply a backward force to the ground, which applies a reaction force forward on the car, to keep the car moving. In fact, we know a few numbers from our car's shop manual. A late model Corvette, for example, has a top speed of about 150 miles per hour and about 240 hp. This means that if you keep your foot all the way down, using up all 240 hp, you can eventually go 150 mph. It takes a while to get there. In this car, you can get to 60 mph in about 6 seconds (if you don't spin the drive wheels), to 100 mph in about 15 seconds, and 150 in about a minute.

All this seems to contradict Newton's first law. What is going on? An automobile moving at constant speed in a straight line on level ground is, in fact, acted on by a number of external forces that tend to slow it down. Without these forces, the car would coast forever as guaranteed by Newton's first law. You must counteract these forces with the engine, which indirectly creates a reaction force that keeps the car going. When the car is going at a constant speed, the net force on the car, that is, the speeding-up forces minus the slowing-down forces, is zero.

The most important external, slowing-down force is air resistance or drag. The second most important force is friction between the tyres and the ground, the so-called rolling resistance. Both these forces are called resistance because they always act to oppose the forward motion of the car in whatever direction it is going. Another physical effect that slows a car down is internal friction in the drive train and wheel bearings. Acting internally, these forces cannot slow the car. However, they push backwards on the tyres, which push forward on the ground, which pushes back by Newton's third law, slowing the car down. The internal friction forces are opposed by external reaction forces, which act as slight braking forces, slowing the car. So, Newton and the Universe are safe; everything is working as it should.

How big are the resistance forces, and what role does horsepower play? The physics of air resistance is very complex and an area of vigorous research today. Most of this research is done by the aerospace industry, which is technologically very closely related to the automobile industry, especially when it comes to racing. We'll slog through some arithmetic here to come up with a table that shows how much horsepower it takes to sustain speed. Those who don't have the stomach to go through the math can skim the next few paragraphs.

We cannot derive equations for air resistance here. We'll just look them up. My source is Fluid Mechanics, by L. D. Landau and E. M. Lifshitz, two eminent Russian physicists. They give the following approximate formula:



The factors in this equation are the following:

Cd = coefficient of friction, a factor depending on the shape of a car and determined by experiment; for a late model Corvette it is about 0.30;
A = frontal area of the car; for a Corvette, it is about 20 square feet;
= Greek letter rho, density of air, which we calculate below;
v = speed of the car.
Let us calculate the density of air using "back of the envelope" methods. We know that air is about 79% Nitrogen and 21% Oxygen. We can look up the fact that Nitrogen has a molecular weight of about 28 and Oxygen has a molecular weight of about 32. What is molecular weight? It is the mass (not the weight, despite the name) of 22.4 litres of gas. It is a number of historical convention, just like feet and inches, and doesn't have any real science behind it. So, we figure that air has an average molecular weight of



I admit to using a calculator to do this calculation, against the spirit of the "back of the envelope" style. So sue me.

We need to convert 1.29 gm/l to pounds of mass per cubic foot so that we can do the force calculations in familiar, if not convenient, units. It is worthwhile to note, as an aside, that a great deal of the difficulty of doing calculations in the physics of racing has to do with the traditional units of feet, miles, and pounds we use. The metric system makes all such calculations vastly simpler. Napoleon Bonaparte wanted to convert the world the metric system (mostly so his own soldiers could do artillery calculations quickly in their heads) but it is still not in common use in America nearly 200 years later!

Again, we look up the conversion factors. My source is Engineering Formulas by Kurt Gieck, but they can be looked up in almost any encyclopaedia or dictionary. There are 1000 litres in a cubic meter, which in turn contains 35.51 cubic feet. Also, a pound-mass contains 453.6 grams. These figures give us, for the density of air



This says that a cubic foot of air weighs 8 hundredths of a pound, and so it does! Air is much more massive than it seems, until you are moving quickly through it, that is.

Let's finish off our equation for air resistance. We want to fill in all the numbers except for speed, v, using the Corvette as an example car so that we can calculate the force of air resistance for a variety of speeds. We get



We want, at the end, to have v in miles per hour, but we need v in feet per seconds for the calculations to come out right. We recall that there are 22 feet per second for every 15 miles per hour, giving us



Now (this gets confusing, and it wouldn't be if we were using the metric system), a pound mass is a phoney unit. A lb-mass is concocted to have a weight of 1 pound under the action of the Earth's gravity. Pounds are a unit of force or weight, not of mass. We want our force of air resistance in pounds of force, so we have to divide lb-mass ft / sec2 by 32.1, numerically equal to the acceleration of Earth's gravity in ft / sec2, to get pounds of force. You just have to know these things. This was a lot of work, but it's over now. We finally get



Let's calculate a few numbers. The following table gives the force of air resistance for a number of interesting speeds:

v (mph) 15 30 60 90 120 150
F (pounds) 3.60 14.5 58.0 130 232 362

We can see that the force of air resistance goes up rapidly with speed, until we need over 350 pounds of constant force just to overcome drag at 150 miles per hour. We can now show where horsepower comes in.

Horsepower is a measure of power, which is a technical term in physics. It measures the amount of work that a force does as it acts over time. Work is another technical term in physics. It measures the actual effect of a force in moving an object over a distance. If we move an object one foot by applying a force of one pound, we are said to be doing one foot-pound of work. If it takes us one second to move the object, we have exerted one foot-pound per second of power. A horsepower is 550 foot-pounds per second. It is another one of those historical units that Napoleon hated and that has no reasonable origin in science.

We can expend one horsepower by exerting 550 pounds of force to move an object 1 foot in 1 second, or by exerting 1 pound of force to move an object 550 feet in 1 second, or by exerting 1 pound of force to move an object 1 foot in 0.001818 seconds, and so on. All these actions take the same amount of power. Incidentally, a horsepower happens to be equal also to 745 watts. So, if you burn about 8 light bulbs in your house, someone somewhere is expending at least one horsepower (and probably more like four or five) in electrical forces to keep all that going for you, and you pay for the service at the end of the month!.

All this means that to find out how much horsepower it takes to overcome air resistance at any speed, we need to multiply the force of air resistance by speed (in feet per second, converted from miles per hour), and divide by 550, to convert foot-lb/sec to horsepower. The formula is



and we get the following numbers from the formula for a few interesting speeds.

v (mph) 30 55 65 90 120 150 200
F (pounds) 14.5 48.7 68.0 130 232 362 644
horsepower 1.16 7.14 11.8 31.3 74.2 145 344

I put 55 mph and 65 mph in this table to show why some people think that the 55 mph national speed limit saves gasoline. It only requires about 7 hp to overcome drag at 55 mph, while it requires almost 12 hp to overcome drag at 65. Fuel consumption is approximately proportional to horsepower expended.

More interesting to the racer is the fact that it takes 145 hp to overcome drag at 150 mph. We know that our Corvette example car has about 240 hp, so about 95 hp must be going into overcoming rolling resistance and the slight braking forces arising from internal friction in the drive train and wheel bearings. Race cars capable of going 200 mph usually have at least 650 hp, about 350 of which goes into overcoming air resistance. It is probably possible to go 200 mph with a car in the 450-500 hp range, but such a car would have very good aerodynamics; expensive, low-friction internal parts; and low rolling resistance tyres, which are designed to have the smallest possible contact patch like high performance bicycle tyres, and are therefore not good for handling.

There's a program called CarTest that already does all of these calculations. It even lets you input your dyno charts at the wheels and simulate your car's performance. Includes drag, wind, tire size, weather, road pavement, etc. There's plenty of discussions on here about that program with test results you can look at.

Bert @ BE had a really great M3 model in CarTest that he used to get really accurate results. So I asked him to run a few simulation models: stock and modified. Here's what he gave me.

Stock: 330 whp
Stock 6MT: top speed 183.5 MPH @ 39720 feet distance.
Stock DCT: top speed 182.6 MPH @ 43930 feet distance

FBO: 392 whp
FBO 6MT: top speed @ 195.3 MPH @ 39250 feet distance.
FBO DCT: top speed @ 194.3 MPH @ 39585 feet distance

[330ciprem]

Originally Posted by spazzyfry123

Damn you're not half bad with that stuff. I ditched the Playstation a while back for the X-Box. I've been a Forza nerd for a while now. I actually think the last Gran Turismo I played is THE one back in the day (2...?)

Forza - the learning curve is insane in that game. I moved to Forza after finishing the latest iteration of Need for Speed! The transition...was not smooth.

[doogee]

Originally Posted by Green-Eggs

Bert @ BE had a really great M3 model in CarTest that he used to get really accurate results. So I asked him to run a few simulation models: stock and modified. Here's what he gave me.

Stock: 330 whp
Stock 6MT: top speed 183.5 MPH @ 39720 feet distance.
Stock DCT: top speed 182.6 MPH @ 43930 feet distance

FBO: 392 whp
FBO 6MT: top speed @ 195.3 MPH @ 39250 feet distance.
FBO DCT: top speed @ 194.3 MPH @ 39585 feet distance

This seems like it may be accurate.

I've reached 300 km/h or 186 mph on the speedo. The car was not struggling either. I was really impressed with how quickly it got there. Wish I had more time to keep going but was forced to lift.

[loveskiing]

Originally Posted by doogee

This seems like it may be accurate.

I've reached 300 km/h or 186 mph on the speedo. The car was not struggling either. I was really impressed with how quickly it got there. Wish I had more time to keep going but was forced to lift.

RCMP problems again bro?