200 Mph
Burning Brakes
Joined: May 2008
Posts: 1,147
Likes: 1
From: Mohegan Lake New York
Here is a simple equation most engineers use for calculating our top speed and for figuring The Horsepower needed for 200mph
ez = 1 + z + z2/2! + z3/3! + z4/4! + z5/5! + z6/6! + Torque ... ,
cos(z) = 1 - z2/2! + z4/4! - z6/6! + z8/8! - z10/10! + Horsepower ... ,
sin(z) = z - z3/3! + z5/5! - z7/7! + z9/9! - z11/11! + drag... .
All three series are valid for all real numbers. We want to accept the first one as valid for all complex numbers z. Then substitute z = xi, expand, use the facts that i2 = -1, i3 = -i, i4 = 1, and so on, and collect real and imaginary parts. You'll see that the real part of exi is just the series for cos(x), and the imaginary part is just the series for sin(x).
z = cos(x) + sin(x) i
and notice that when x = 0, z = 1. Then differentiate,
dz/dx = -sin(x) + cos(x) i
dz/dx = sin(x) i2 + cos(x) i
dz/dx = [cos(x) + sin(x) i]i
dz/dx = zi
(1/z)dz/dx = i
ln(z) = xi + C
for some constant C, by indefinite integration. Now use the fact that when x = 0, z = 1, to conclude that C = 0. Thus
ln(z) = xi
z = exi
exi = cos(x) + sin(x) i
|z| = sqrt(a2+b2)
z/|z| is then a complex number whose absolute value is 1. Then there is some t such that
cos(t) = a/sqrt(a2+b2)
sin(t) = b/sqrt(a2+b2)
tan(t) = b/a,
t = arctan(b/a)
You can always choose t in the range 0 <= t < 2 to satisfy these conditions. There are two t values in this range with tangent b/a, which differ by . Pick t > if and only if b < 0. Pick t = if and only if b = 0 and a < 0. Then
z = sqrt(a2+b2)[a/sqrt(a2+b2) + bi/sqrt(a2+b2)]
= sqrt(a2+b2)[cos(t) + sin(t) i]
= |z|eti
= eln|z|+ti
ez = 1 + z + z2/2! + z3/3! + z4/4! + z5/5! + z6/6! + Torque ... ,
cos(z) = 1 - z2/2! + z4/4! - z6/6! + z8/8! - z10/10! + Horsepower ... ,
sin(z) = z - z3/3! + z5/5! - z7/7! + z9/9! - z11/11! + drag... .
All three series are valid for all real numbers. We want to accept the first one as valid for all complex numbers z. Then substitute z = xi, expand, use the facts that i2 = -1, i3 = -i, i4 = 1, and so on, and collect real and imaginary parts. You'll see that the real part of exi is just the series for cos(x), and the imaginary part is just the series for sin(x).
z = cos(x) + sin(x) i
and notice that when x = 0, z = 1. Then differentiate,
dz/dx = -sin(x) + cos(x) i
dz/dx = sin(x) i2 + cos(x) i
dz/dx = [cos(x) + sin(x) i]i
dz/dx = zi
(1/z)dz/dx = i
ln(z) = xi + C
for some constant C, by indefinite integration. Now use the fact that when x = 0, z = 1, to conclude that C = 0. Thus
ln(z) = xi
z = exi
exi = cos(x) + sin(x) i
|z| = sqrt(a2+b2)
z/|z| is then a complex number whose absolute value is 1. Then there is some t such that
cos(t) = a/sqrt(a2+b2)
sin(t) = b/sqrt(a2+b2)
tan(t) = b/a,
t = arctan(b/a)
You can always choose t in the range 0 <= t < 2 to satisfy these conditions. There are two t values in this range with tangent b/a, which differ by . Pick t > if and only if b < 0. Pick t = if and only if b = 0 and a < 0. Then
z = sqrt(a2+b2)[a/sqrt(a2+b2) + bi/sqrt(a2+b2)]
= sqrt(a2+b2)[cos(t) + sin(t) i]
= |z|eti
= eln|z|+ti
Le Mans Master
Joined: Mar 2002
Posts: 5,955
Likes: 161
From: PNW
Forgot to say a while back for those who where interested, the basic formulas for the required RWHP to overcome aerodrag and rolling resistance is shown below. Notice that power = force x velocity, which is the same as (force x distance)/time = work per time. Also notice that the required HP to overcome aerodrag is a CUBIC function of velocity ... that's why it takes big HP to go over 200 MPH.
Required RWHP = Aerodrag RWHP + Rolling Resistance RWHP
Power = RWHP = force X velocity = (lbf)(ft/sec)/550
Aerodrag RWHP = (Cd)(A)(d)(V^3)/2/Gc/550
Cd = drag coefficient (unitless)
A = frontal area (ft^2)
d = air density (lbs/ft^3)
V = velocity (ft/sec)
Gc = gravitational constant (32.2 ft/sec^2)
550 (1 HP, mechanical = 550 ft-lbf/sec)
Rolling Resistance RWHP = (Cr)(W)(V)/550
Cr = rolling coefficient (unitless)
W = vehicle's weight (lbs)
V = velocity (ft/sec)
550 (1 HP, mechanical = 550 ft-lbf/sec)
Required RWHP = Aerodrag RWHP + Rolling Resistance RWHP
Power = RWHP = force X velocity = (lbf)(ft/sec)/550
Aerodrag RWHP = (Cd)(A)(d)(V^3)/2/Gc/550
Cd = drag coefficient (unitless)
A = frontal area (ft^2)
d = air density (lbs/ft^3)
V = velocity (ft/sec)
Gc = gravitational constant (32.2 ft/sec^2)
550 (1 HP, mechanical = 550 ft-lbf/sec)
Rolling Resistance RWHP = (Cr)(W)(V)/550
Cr = rolling coefficient (unitless)
W = vehicle's weight (lbs)
V = velocity (ft/sec)
550 (1 HP, mechanical = 550 ft-lbf/sec)
Last edited by ZeeOSix; Dec 29, 2008 at 09:56 PM.
Instructor
Joined: Nov 2008
Posts: 156
Likes: 0
From: Manning SC
I'm telling you what it takes. You need an air dam, at least 750RWHP and the right gearing and you can make a C5 go 225MPH over a measured mile. John Lingenfelter did it in 2004 with a 2000 C5 TT with a manual transmission, 18" wheels and an air dam up front.
Le Mans Master
Joined: Mar 2002
Posts: 5,955
Likes: 161
From: PNW
I'm sure it does, and in order to hit 225 MPH at the end of one mile from a dead stop (I'm assuming that's what you meant), it will take more HP than it would take to hit 225 with much more distance to get there. 225 MPH in a standing mile is quite a feat.
Instructor
Joined: Nov 2008
Posts: 156
Likes: 0
From: Manning SC
Use your head man. It was a flying mile. John did it and it ran in an April 2004 magazine. Can't remember which one. I'm pretty familiar with that car. It was averaged over two runs. It's not hard to do but you need to be safe. I don't know what happened to the dam. And I've forgotten who built the tranny but it wasn't anything terribly exclusive. Just a built 6 speed.
Le Mans Master
Joined: Mar 2002
Posts: 5,955
Likes: 161
From: PNW
You didn't specify, so could very well have been a standing mile. Christ man, I know it's gonna take ~600 RWHP to go 225 MPH with enough room to get there, so it's not out of the question to go 225 in a standing mile with 750 RWHP. Sorry, but Mr. Spock went out for a couple of beers earlier tonight, otherwise I would have had him crunch the numbers and conclude if it was a standing or flying mile. 
Last edited by ZeeOSix; Dec 28, 2008 at 12:14 AM.
Instructor
Joined: Nov 2008
Posts: 156
Likes: 0
From: Manning SC
That did sound abrupt. Sorry didn't mean it that way. Shoulda put a smiley there. I don't know of anyone who has broken the 200 MPH barrier in a street run vette over a 1/4 mile. Out of the loop anymore but I doubt anyone takes a vette with a IRS and goes over 200. Am I wrong about that? And that's a touchy subject so sorry if I offend anyone.
Le Mans Master
Joined: Mar 2002
Posts: 5,955
Likes: 161
From: PNW
That did sound abrupt. Sorry didn't mean it that way. Shoulda put a smiley there. I don't know of anyone who has broken the 200 MPH barrier in a street run vette over a 1/4 mile. Out of the loop anymore but I doubt anyone takes a vette with a IRS and goes over 200. Am I wrong about that? And that's a touchy subject so sorry if I offend anyone.
Doing 200 MPH in a standing 1/4 mile vs. in a standing mile are entirely two different feats.
A 750 rwhp (~880 fwhp) car that weighs 3400 lbs with driver should hit ~145 - 150 MPH in a 1/4 mile. That means it only has to go 50 - 55 MPH faster in the next 3/4 mile. IMO, entirely possible. Doing a flying mile would make it even easier to do with that much power and the right gearing.
http://www.stealth316.com/2-calc-hp-et-mph.htm
http://www.autocalculator.org/Engine...alculator.aspx
Last edited by ZeeOSix; Dec 30, 2008 at 11:10 PM.
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Drifting
Joined: Jan 2005
Posts: 1,517
Likes: 0
Thread Starter
Le Mans Master
Joined: Nov 2005
Posts: 5,451
Likes: 2
From: East Peoria Illinois
Good info. It can be seen that 4.10s are too low for a top speed run as it will only hit 165~170 at redline, and 6th gear is still useless due to the huge ratio gap between 5th and 6th.
For a top speed run, the differential should be changed to allow max HP usage from 5th gear.
A 3.42 rear end used in the spreadsheet gives ~205 in 5th gear at 6700 RPM. That's not a bad combo.
A Z06 tranny is actually setup worse for top end in 5th gear, as it's ratio is 0.84, and with a 3.42 rear end will only go ~173 MPH at 6500 RPM. In contrast, the 0.74 5th gear ratio gives ~199 MPH at 6500 RPM.
For a top speed run, the differential should be changed to allow max HP usage from 5th gear.
A 3.42 rear end used in the spreadsheet gives ~205 in 5th gear at 6700 RPM. That's not a bad combo.
A Z06 tranny is actually setup worse for top end in 5th gear, as it's ratio is 0.84, and with a 3.42 rear end will only go ~173 MPH at 6500 RPM. In contrast, the 0.74 5th gear ratio gives ~199 MPH at 6500 RPM.
Thread Starter
Le Mans Master
Joined: Nov 2005
Posts: 5,451
Likes: 2
From: East Peoria Illinois
The RPM numbers I quoted were actually specifically for your gearing... stock Z06 is somewhere in the 3.80 and 4.00 equivelant range, depending on the gear you are in.
I haven't modded much of anything since the summer cam swap... I've just been swapping out worn out odds and ends (seat bottom leather and foam, broken drivers mirror glass, etc.) Nothing really exciting, heh. Your car looks like it's been coming together well.
I haven't modded much of anything since the summer cam swap... I've just been swapping out worn out odds and ends (seat bottom leather and foam, broken drivers mirror glass, etc.) Nothing really exciting, heh. Your car looks like it's been coming together well.
Le Mans Master
Joined: Mar 2002
Posts: 5,955
Likes: 161
From: PNW
Transmission Gear ratios
Gear LS1 / MN6 ....|.... LS6 / M12 6-speed
1st 2.66:1 ....|.... 2.97.1
2nd 1.78:1 ....|.... 2.07:1
3rd 1.30:1 ....|.... 1.43:1
4th 1.00:1 ....|.... 1.00:1
5th 0.74:1 ....|.... 0.84:1
6th 0.50:1 ....|.... 0.56:1
reverse 2.90:1 ....|.... 3.28:1
Last edited by ZeeOSix; Dec 31, 2008 at 02:02 AM.
Le Mans Master
Joined: Oct 2006
Posts: 7,484
Likes: 2
From: Dayton, OH HAWG: "this is Off Topic...it can get a bit north of care bears and strawberry shortcake in here"
St. Jude Donor '08-'09-'10-'11
It'll be funny when our forum genius in here realizes that horsepower is actually an imaginary number derived from torque...
Hey, genius, you keep on saying HP HP HP, and a lot of blah blah blah, but if you were really smart, you'd see that HP will not exist without torque. It's actually a transpose. So, in short, torque is the only measurement of power output from an engine. well, that and thermal output, anyway, but you don't transfer thermal loads directly into forward motion in most cases.
Anyway, think about this logically. If the formula that derives horsepower is directly dependent on the two variables of torque and rpm, then you will never have a change in horsepower without a change in torque or RPM. So when you say that horsepower is what matters in top speed, you are only correct insofar as you can't really not be correct. You can still be an idiot, though.
Top speed is dependent on torque, RPM's, and gearing. You can, of course, use the transpose formula for calculating horsepower and say the same thing in this manner: Top speed is dependent on horsepower and gearing. See the relationship? You are only wrong when you argue that it's not a matter of torque, but a matter of horsepower. If the RPM and gearing remain the same, it's a matter of torque, which increases the amount of horsepower.
So when you screamed "TOP SPEED is.... REAR WHEEL HORSE POWER, AERODYNAMIC DRAG + FRONT TIRE ROAD FRICTION + FRONT WHEEL BEARING FRICTION, AND GEARING" you could also have not been an idiot and said "TOP SPEED is.... REAR WHEEL TORQUE, ENGINE RPM, AERODYNAMIC DRAG + FRONT TIRE ROAD FRICTION + FRONT WHEEL BEARING FRICTION, AND GEARING"
Horsepower is a relational number, calculated from two other variables, the ones that matter. So stop being an idiot, and go read a book or something.
I learned all this on the back of a cereal box in Physics class, though...
Hey, genius, you keep on saying HP HP HP, and a lot of blah blah blah, but if you were really smart, you'd see that HP will not exist without torque. It's actually a transpose. So, in short, torque is the only measurement of power output from an engine. well, that and thermal output, anyway, but you don't transfer thermal loads directly into forward motion in most cases.
Anyway, think about this logically. If the formula that derives horsepower is directly dependent on the two variables of torque and rpm, then you will never have a change in horsepower without a change in torque or RPM. So when you say that horsepower is what matters in top speed, you are only correct insofar as you can't really not be correct. You can still be an idiot, though.
Top speed is dependent on torque, RPM's, and gearing. You can, of course, use the transpose formula for calculating horsepower and say the same thing in this manner: Top speed is dependent on horsepower and gearing. See the relationship? You are only wrong when you argue that it's not a matter of torque, but a matter of horsepower. If the RPM and gearing remain the same, it's a matter of torque, which increases the amount of horsepower.
So when you screamed "TOP SPEED is.... REAR WHEEL HORSE POWER, AERODYNAMIC DRAG + FRONT TIRE ROAD FRICTION + FRONT WHEEL BEARING FRICTION, AND GEARING" you could also have not been an idiot and said "TOP SPEED is.... REAR WHEEL TORQUE, ENGINE RPM, AERODYNAMIC DRAG + FRONT TIRE ROAD FRICTION + FRONT WHEEL BEARING FRICTION, AND GEARING"
Horsepower is a relational number, calculated from two other variables, the ones that matter. So stop being an idiot, and go read a book or something.
I learned all this on the back of a cereal box in Physics class, though...
Burning Brakes
Joined: May 2006
Posts: 1,049
Likes: 2
From: Houston TEXAS
Speaking of drag and gearing------I'm getting my A4 ready to take a shot at the 200 patch. What are some good non-permanant ways to lower drag. I have heard
1. Lower the car
2. Shave the mirrors
3. Tape off openings (but which openings??)
Should I an inch off the air dam to reduce the amount of air coming in under the hood to the radiator?
Any other suggestions
Also - I currently have a 273 with my 3-4 shift point set at 180. Is this the ideal gear for an A4 with this goal in mind? Or would a 315 or 342 be better. Thanks to all-
1. Lower the car
2. Shave the mirrors
3. Tape off openings (but which openings??)
Should I an inch off the air dam to reduce the amount of air coming in under the hood to the radiator?
Any other suggestions
Also - I currently have a 273 with my 3-4 shift point set at 180. Is this the ideal gear for an A4 with this goal in mind? Or would a 315 or 342 be better. Thanks to all-
Drifting
Joined: Oct 2000
Posts: 1,396
Likes: 0
From: Sacramento CA
Thoughts
You ask about tapeing all the seams hood/lights. fold the mirrors in or better yet take them off.
You ask about what to do with the front of the car. Best thing to do is make it a front breather and add a air dam to the front of the car. This sucks down to the ground at speed.
See the pic of my C4 Open Road racecar:
Then vent your hood:
I have not run the C5 to top speed yet, but my C4 has hit 206, but not from a standing start. Which I think is what you are attemting to do. I have right at 600rwhp in the C4, but I am loseing some top end with the wing. I need the wing though since I average 170 for 90 miles and make turns. If you do the front as described above you might find you need to have some kind of spioler on the rear to balance the downforce you have added to the front.
Jeffy'
You ask about what to do with the front of the car. Best thing to do is make it a front breather and add a air dam to the front of the car. This sucks down to the ground at speed.
See the pic of my C4 Open Road racecar:
Then vent your hood:
I have not run the C5 to top speed yet, but my C4 has hit 206, but not from a standing start. Which I think is what you are attemting to do. I have right at 600rwhp in the C4, but I am loseing some top end with the wing. I need the wing though since I average 170 for 90 miles and make turns. If you do the front as described above you might find you need to have some kind of spioler on the rear to balance the downforce you have added to the front.
Jeffy'
Le Mans Master
Joined: Mar 2002
Posts: 5,955
Likes: 161
From: PNW
It'll be funny when our forum genius in here realizes that horsepower is actually an imaginary number derived from torque...
Hey, genius, you keep on saying HP HP HP, and a lot of blah blah blah, but if you were really smart, you'd see that HP will not exist without torque. It's actually a transpose. So, in short, torque is the only measurement of power output from an engine. well, that and thermal output, anyway, but you don't transfer thermal loads directly into forward motion in most cases.
Hey, genius, you keep on saying HP HP HP, and a lot of blah blah blah, but if you were really smart, you'd see that HP will not exist without torque. It's actually a transpose. So, in short, torque is the only measurement of power output from an engine. well, that and thermal output, anyway, but you don't transfer thermal loads directly into forward motion in most cases.
So exactly where did I say that HP wasn't a DERIVED unit of measurement? Can you really comprehend English? ... doesn't seem like it to me.
Anyway, think about this logically. If the formula that derives horsepower is directly dependent on the two variables of torque and rpm, then you will never have a change in horsepower without a change in torque or RPM. So when you say that horsepower is what matters in top speed, you are only correct insofar as you can't really not be correct. You can still be an idiot, though.
... are you Quasar's Dad? Dude, what do you think "torque, RPM" is ?? .... it's HORSEPOWER. Wow, I'm pretty sure you're really wrapped around the axle or higher than a kite on this stuff. Aren't you the retired GM engineer here? Wow.You can, of course, use the transpose formula for calculating horsepower and say the same thing in this manner: Top speed is dependent on horsepower and gearing. See the relationship? You are only wrong when you argue that it's not a matter of torque, but a matter of horsepower. If the RPM and gearing remain the same, it's a matter of torque, which increases the amount of horsepower.
So when you screamed "TOP SPEED is.... REAR WHEEL HORSE POWER, AERODYNAMIC DRAG + FRONT TIRE ROAD FRICTION + FRONT WHEEL BEARING FRICTION, AND GEARING" you could also have not been an idiot and said "TOP SPEED is.... REAR WHEEL TORQUE, ENGINE RPM, AERODYNAMIC DRAG + FRONT TIRE ROAD FRICTION + FRONT WHEEL BEARING FRICTION, AND GEARING"
Horsepower is a relational number, calculated from two other variables, the ones that matter. So stop being an idiot, and go read a book or something.
I learned all this on the back of a cereal box in Physics class, though...
Horsepower is a relational number, calculated from two other variables, the ones that matter. So stop being an idiot, and go read a book or something.
I learned all this on the back of a cereal box in Physics class, though...
I think that cereal box had it all wrong ... or you just couldn't understand it. Aren't you glad you responded with your attacks claiming everyone is all wrong with your pompous BS that doesn't even make sense? Have a good one ... "genius".
PS -- Mr. Genius, please entertain and show me exactly how a car can go faster on top end at peak torque point than at peak HP point. I really want to see the proof.
Last edited by ZeeOSix; Dec 31, 2008 at 04:04 PM.
Le Mans Master
Joined: Mar 2002
Posts: 5,955
Likes: 161
From: PNW
... what kind of RWHP is that C4 making? As you have said, the rear spoiler is going to add some significant drag, which means even more HP is required to hit 206.
Last edited by ZeeOSix; Jan 1, 2009 at 02:32 PM.
Instructor
Joined: Jul 2008
Posts: 207
Likes: 3
From: Fort Walton Beach Florida
Well, I assume you're trying to talk to me ... If not, then you still need a response from someone who needs to set you straight. By the way, you better change your handle, because you're not even close to a "genius". Maybe something with the letters " l-e-a-h-o " (not necessarily in that order) in it might be more fitting.
So exactly where did I say that HP wasn't a DERIVED unit of measurement? Can you really comprehend English? ... doesn't seem like it to me.
Wow... are you frickin' sauced out? Who said torque and speed isn't related or doesn't define HP? Can you even understand what's being discussed here? And BTW, PEAK HP (along with gearing, aeros, etc, etc) is what determines a vehicles top speed ... NOT peak torque, as you say in the next sentence.
... are you Quasar's Dad? Dude, what do you think "torque, RPM" is ?? .... it's HORSEPOWER. Wow, I'm pretty sure you're really wrapped around the axle or higher than a kite on this stuff. Aren't you the retired GM engineer here? Wow.
Psychobabble ... period. Isn’t that what I’ve been saying. What’s your problem? Listen carefully, torque and HP are related ... you know that, right? But it's ultimately HP that determines a vehicles top end speed. Period.
Ummm ... I think it's YOU that needs to re-educate yourself from when you tried to figure this stuff out back in 1959. I think that cereal box had it all wrong ... or you just couldn't understand it.
Aren't you glad you responded with your attacks claiming everyone is all wrong with your pompous BS that doesn't even make sense? Have a good one ... "genius".
PS -- Mr. Genius, please entertain and show me exactly how a car can go faster on top end at peak torque point than at peak HP point. I really want to see the proof.
So exactly where did I say that HP wasn't a DERIVED unit of measurement? Can you really comprehend English? ... doesn't seem like it to me.
Wow... are you frickin' sauced out? Who said torque and speed isn't related or doesn't define HP? Can you even understand what's being discussed here? And BTW, PEAK HP (along with gearing, aeros, etc, etc) is what determines a vehicles top speed ... NOT peak torque, as you say in the next sentence.
... are you Quasar's Dad? Dude, what do you think "torque, RPM" is ?? .... it's HORSEPOWER. Wow, I'm pretty sure you're really wrapped around the axle or higher than a kite on this stuff. Aren't you the retired GM engineer here? Wow.Psychobabble ... period. Isn’t that what I’ve been saying. What’s your problem? Listen carefully, torque and HP are related ... you know that, right? But it's ultimately HP that determines a vehicles top end speed. Period.
Ummm ... I think it's YOU that needs to re-educate yourself from when you tried to figure this stuff out back in 1959.
I think that cereal box had it all wrong ... or you just couldn't understand it. Aren't you glad you responded with your attacks claiming everyone is all wrong with your pompous BS that doesn't even make sense? Have a good one ... "genius".
PS -- Mr. Genius, please entertain and show me exactly how a car can go faster on top end at peak torque point than at peak HP point. I really want to see the proof.
Le Mans Master
Joined: Mar 2002
Posts: 5,955
Likes: 161
From: PNW
It's not a Vette, but just goes to show what 750 crank HP (probably around 635 rwhp if a manual tranny using 15% drivetrain loss) can do if geared right ... officially 228 mph.
http://www.bmwtuningmag.com/g-power-...isting-record/
PS ... for Mr. "Genius", my calculations show it takes ~ 640 rwhp to go 228 mph for a car like this. And I didn't even know how much torque this ccar makes. Ya know why? -- because torque at this point is unimportant if you know the HP. ONLY HP matters for top end. Use the equations in post #182 if you don't believe it. Go figure.
http://www.bmwtuningmag.com/g-power-...isting-record/
PS ... for Mr. "Genius", my calculations show it takes ~ 640 rwhp to go 228 mph for a car like this. And I didn't even know how much torque this ccar makes. Ya know why? -- because torque at this point is unimportant if you know the HP. ONLY HP matters for top end. Use the equations in post #182 if you don't believe it. Go figure.
Last edited by ZeeOSix; Jan 3, 2009 at 01:33 AM.