Terry Humiston

I tend to go a little overboard with formulas, calculations and such so I will leave out as much of that stuff as possible. As I am often told, it is boring. First a couple of notes: I am ignoring any tire deflection because it will be almost the same in all cases so it cancels out and the torque figures are engine flywheel times the over all ratio ignoring driveline loss. Again, it will be almost the same in all cases so it cancels out.

If we say the 04 C5 6speed coupe has a top speed of 175 mph we get the following:

Tire of 275/40-18 is 26.7” tall and goes 6.99 feet per revolution
Axle ratio of 3.42 times the fifth gear ratio of 0.74 equals 2.53 overall ratio
5200 RPM = 163 mph an axle torque of 885 (350x2.53)
6000 RPM = 188 mph an axle torque of 750 +/-
It would seem that while this example has the gear to reach over 175MPH it lacks the power to over come the wind.

If we say the 04 Z06 6speed has a top speed of 175 mph we get the following:

Tire of 295/35-18 is 26.1” tall and goes 6.84 feet per revolution
Axle ratio of 3.42 times the fifth gear ratio of 0.84 equals 2.87 overall ratio
6000 RPM = 162 mph an axle torque of 1019 (355x2.87)
6500 RPM = 176 mph an axle torque of 890
It would seem that the Z06 reaches max speed right at redline and would appear to run out of gear or RPM. I would bet, it is also right up against the power vs. wind limit too.

When we look at the new C6 LS2 Z51 what do we get?

Tire of 285/35-19 is 26.8” tall and goes 7.00 feet per revolution
Axle ratio of 3.42 times the fifth gear ratio of 0.71 equals 2.43 overall ratio
5500 RPM = 180 mph an axle torque of 887
6000 RPM = 196 mph an axle torque of 850
6500 RPM = 212 mph an axle torque of not enough.
It would seem that like the regular C5 the C6 will run out of power before it runs out of gear. It would seem this balance is going to come at just over 180, but no 190… but what if?

We take a C6 LS2 Z51 and install a set of 3.73

Tire of 285/35-19 is 26.8” tall and goes 7.00 feet per revolution
Axle ratio of 3.73 times the fifth gear ratio of 0.71 equals 2.65 overall ratio
6000 RPM = 180 mph an axle torque of 928 (pulling harder here)
6500 RPM = 195 mph an axle torque of 800? Not enough?
Looks like a C6 with 3.73 would go well up into the 180s maybe 190 mph.

TTRotary

One small problem Terry: The C6 Z51 will use the M12 transmission, whose 5th gear is 0.84. So I think the top speed champ will be the base model with the 0.71 5th gear.

SWCDuke

First, you should use actual specified revs per mile, not the unloaded circumference. (Due to deflection under load actual tire revs per mile are about two to three percent greater than what you calculate from the inflated diameter/circumference.) The rear tires on C6 are about 769 revs/mi - based on a spec for a same size Pirelli. I don't have a Goodyear spec, but it will be within a handful of revs per mile if not exactly the same.

Required horsepower is a function of the cube of speed, so you can ballpark C6 top speed as follows given that 350 HP C5 coupes have been tested at 175.

cube root (400/350) x 175 = 183.

At this speed the base six speed will be at just over 5900. With Z-51 gearing it will be more like 5700, but given the flat nature of the LS2 power curve it should pull.

Top speed is dependent on the test venue, especially wind and temperature, but I expect when the mags start testing they will record top speeds of at least 179-180 MPH.

Also consider that the tires on Corvettes are Y-rated, so I expect GM may have programmed a 186 MPH limiter into the electronics.

Duke

Terry Humiston

From the spec. I have seen the C6 Z51 is not quite the same as the M12. http://www.c6registry.com/specifications/index.htm

This the source I found...

Terry Humiston

Duke,

In my C6 example 7 feet per rev. would yield 754 rev per mi vs your 769. A difference of about 2% Is the rev per mile spec at what load & at what speed, both would effect. My purpose was not to nit pick the details. The ulitmate top speed is not so much a function of HP as it is axle torque. The distinction being the right gear ratios will bring more torque to bear as the vehicle reaches equalibrium between power & wind resistance.


[Modified by Terry Humiston, 1:45 PM 1/7/2004]

TTRotary

Interesting, thanks.

I wonder if they transposed the 0.71 and 0.74. Seems odd, given the shorter sixth cog on the Z51 box. Either way, there is enough gear for 180+, which I think the car is capable of.

Runge_Kutta

I posted this last week ...
http://forums.corvetteforum.com/zero...=719424&page=2

======================================== =======================================

A manual C5 can do about 174 hp with about 300 rwhp (at that speed,
I think). A manual C6 ought to have about 400*0.85 = 340 rwhp, hopefully
at top speed but this depends on gearing. The power required for
the car to move at constant velocity and level ground could reasonably
be written as

power = a*v^3 + b*v^2 + c*v + d

but as v (velocity) becomes large, the quadratic,
linear and constant terms have minor effect as long
as the constants (a, b, c, and d) are determined at
a nearby velocity point. I believe that the Cd*A of
the C6 is 2% better than C5 but I'd really need to know
how the area is determined (this is subjective and
reasonable aerodynamicists may choose slightly different
areas).

OK, enough caveats. Solve for a and you get 0.0000569473 or
0.0000558084 for C6.

At 340 rwhp, I get 182.639 mph
At 350 rwhp, I get 184.412 mph
At 360 rwhp, I get 186.152 mph

Again, I have assumed that these rwhp values are available at
the top speed. Since quadratic and lower terms have been dropped,
these numbers are a bit optimistic.

======================================== =======================================

Timmy's C5

Interesting topic. You guys and your math rule! Maybe somebody can tell me why the Ferrari 360 with more weight, less horspower and worse aeros (higher cd) can be so much faster then either the C5 or the C6?

SWCDuke

No, speed is a function of the cube root of power, which is energy per unit time, and the generic formula was posted. Torque is not a dynamic measurement, power is. Power is also equal to drive thrust times velocity (with the proper factors to maintain dimensional homogeneity), and top speed is reached when drive trust equals total drag.

Duke

Dsob15

It isn't.

Runge_Kutta

Yes, you can look at it as a force balance or look at it as an energy
balance too. I am told rolling resistance is essentially

F_{r} = c1*v

The basis of that is, I assume that viscous stresses in bearings are proportional
to velocity gradients. Aerodynamic drag (skin friaction and pressure) is

F_{a} = c2*v^2

where c2 (and c1 below) are some constants. Then the net force that the engine
must balance includes at least

F = c2*v^2 + c1*v

and hence the rate of energy balance (P = F dot v) iincludes at least

Power = c2*v^3 + c1*v^2

Ultimately, it seems easiest to just use a third-order polynomial
and curve fit without trying to bookkeep every teeny weeny
force or power balance term. As v gets large, the energy balance
is dominated by the v^3 term. Also, what if the friction in the
bearings is due to a non-Newtonian fluid and the friction has
some bizarre relation to the angular velocity of the wheel. What a
mess!! That's another reason to just curve fit a polynomial through
the data.

SWCDuke

Yes, rolling resistance is a function of velocity and aero resistance a function of veleocity squared. Multiply by speed to determine required power and the cubic term dominates.

By running coast down tests on a level surface with different weights (been there, done that) one can develop an empirical equation to determine the power required to achieve a given speed for a given car, and if you have data for a lot of cars you can get a pretty good feel for the coefficients and develop good estimates for new models.

The bottom line is that US manufacturer's are not too concerned with top speed. It's somewhat of a trophy in Europe because there are some places where you can legally run at top speed in Europe, but not in the US.

If anything, the Corvette engineers are facing an engineering/legal barrier with the Y-rated tires that are OE on Corvettes.

Duke

LittleBoyBlu99

SWCDuke

What do you think the top speed of a F360 is? Quote the value and your source.

Duke

Timmy's C5

The top speed of the Ferrari is quoted on several web sites as being 189 mph. Forza, the Ferrari magizine, stated the top speed of the 360 to be 185 more then once (Aug. 1999 for example). Road and Track found the top speed of the Z06 to be 171 in one case (Aug 2000) and 174.8 on another (Nov. 2000). Motor Trend in June 2003 cited the top speed of the Z06 to be 174.

Don't get me wrong here, I'm not knocking the Corvette, I am only wondering how the Ferrari finds that top speed.

Daryl

Very interesting subject. Don't stop now.

Terry Humiston

If Let me try the same approach that I used on the Vette and apply it to the 360

Tire 275/40-18 is 26.7 tall and goes about 7 ft per revolution
Axle ratio of 4.44 times the six gear ratio of 0.85 equals 3.77 overall ratio
8500 RPM = 179 mph an axle torque of 920 lb.ft.

Seems a 360 would top out very close to 180 mph bouncing off the rev limiter. Sorry no 189, it would need 9000 RPM to do it. It has the needed 900 + lbs of twist needed to push back the wind. How does a wimpy 360 have more torque that the Vette? In a word, gears. They are the key to top speed. The 360 makes 395 HP at 8500 RPM and 244 lb.ft. of torque at 8500. When we multiply 244 by the 3.77 overall ratio we get 920 lb.ft. of twist at 179 mph. The 360 is about the same weight as the Z06 and while it may have a slightly higher Cd it also probably has a slightly smaller cross section.

Timmy's C5

Thanks Terry.

BTW, I measured the frontal area of both cars once and found the Ferrari to be very slightly larger then the Corvette. Took photo's of 1/18 the scale model of each with a very long telephoto lens to reduce distortion, then printed enlargements and carefully cut out both. For refernce, I encluded in the photos a 2" X 2'' machinist square, which at that scale represented 1 sq. yard. For the life of me, I can't find my results anywhere!

Scissors

I went Ferrari top speed hunting and found that, though several sites quote a 189 number, Ferrari's actualy official number that they give the dealers is 183.

Timmy's C5

BTW,

Road and Track still lists the top speed of the Ferrari at 189 in the back of each mag. Maybe they read the same websites I do.