| Author |
Message |
Mark Eberhardt (Me_k)
Member
Username: Me_k
Post Number: 470
Registered: 5-2002
| | Posted on Sunday, April 06, 2003 - 4:48 pm: | |
Mike,
I'm surprised, but the math is right. I can't find my dyno graph, I know it drops about 10 HP between 7000 and 7500. So that puts the torque down around 160@7500, but it doesn't change change anything. It looks like I need to start shifting at redline. |
Mike Charness (Mcharness)
Member
Username: Mcharness
Post Number: 426
Registered: 8-2002
| | Posted on Sunday, April 06, 2003 - 3:44 pm: | |
I got a response from my friend Tom, of Speedturn Racing. It is posted below. I've told him meanwhile that his presumption about tire size is incorrect (we have 16" wheels).
\\\\\\\\\\\\\\\\\\\\\\/////////////////////////
Mike (and other Ferrari folks):
I've looked at the numbers listed here for your transmission ratios and your engine torque and power versus rpm. 190 ft-pound @ 5000 to 5500rpm, 180 ft-pound @ 6500rpm, and 170 ft-pound @ 7500 rpm.
1st 3.419 trans gears
2nd 2.359
3rd 1.693
4th 1.244
5th 0.919
It is interesting to me that Ferrari made each ratio close to 70% of the previous ratio.
2nd/1st = 0.69, 3rd/2nd = 0.72, 4th/3rd = 0.73 and 5th/4th = 0.74
If you want to know how far your revs drop when you shift, then multiply your revs by the above ratios to find the new revs. For example, if you rev 1st gear out to 7500 rpm, then the revs when you engage 2nd gear are 7500x0.69 = 5170 rpm
ring and pinion 65/14 = 4.06 = rear axle gear ratio
I assume that you have 225/50x15 rear tires, they have about 24" diameter, 12" radius, 1foot radius.
Tire radius r = 1 foot
Let TQ = engine torque in foot-pounds
The transmission multiplies engine torque, and feeds that torque to the rear axle gears, and they further multiply the torque, and those gears rotate the back tires.
Acceleration comes from force F pushing your forward.
force F = (TQ x TransRatio x RearAxleRatio ) / (Tire Radius)
Since rear axle ratio and tire diameter and radius are always the same, no matter what gear your tranny is in, then tires and rear axle ratio have no effect on determining the optimal shift rpm, because they are always constant.
Therefore, the force you have available to accelerate your car reduces down to
EngineTorque x Trans Ratio
Every time you shift to a higher gear, your trans ratio gets smaller, so the product of Engine Torque x Trans Ratio gets smaller, so you will accelerate slower every time you go to a higher gear.
Let us look at the 1st to 2nd gear shift at different engine rpms.
At 6500 rpm in 1st gear, the engine is making 180 ft-pound,
and coming out of the tranny is 180 x 3.419 = 615 ft-pound of energy.
When we shift to 2nd, engine revs drop to 4500 rpm, off the scale of your torque curve.
Lets assume the engine makes 185 ft-pounds of torque at 4500 rpm.
In 2nd gear, coming out of the tranny is 185 x 2.359 = 435 ft-pound of energy.
This is much, much less than the 615 ft-pound of energy you had in first gear, so you lost energy by shifting early. It is better to keep revving the engine higher in the lower gear.
Now lets rev first gear out higher, and see what happens
At 7500 rpm in 1st gear, the engine makes 170 ft-pound x 3.419 = 581 ft-pounds of energy coming out of the transmission.
Shifting into 2nd, revs drop to 5170 rpm, the engine makes 190 ft-pounds, and the energy coming out of the trans is 190 x 2.359 = 448 ft=pounds.
Even though the engine made less torque at the higher revs in 1st gear, the energy coming out of trans is still much greater in 1st than it is in 2nd gear, so you have more energy available to accelerate you faster. Another benefit of higher shifts is that the energy in 2nd is better at the higher revs than it is at the lower revs, so your 2nd gear will pull faster at the higher revs than the lower revs.
Saying it another way: even though engine torque is decreasing at the higher revs, there is still more torque energy coming out of the transmission by staying in the lower gear and revving it higher.
That is a lot of arithmetic to try and explain what is happening, but the numbers don't lie.
The only exception to this method is when you have way, way more power than you have traction at the rear wheels, and your tires spin really bad when you shift into 2nd gear. For cars with this much power, sometimes they will get better acceleration with low rev shifts just because that will produce less wheel spin.
Tom Turner PE
Speedturn Racing |
Hans E. Hansen (4re_gt4)
Intermediate Member
Username: 4re_gt4
Post Number: 1039
Registered: 4-2002
| | Posted on Thursday, April 03, 2003 - 11:38 pm: | |
Yeah, Ferrari's are blessed with some decent gear splits. However, to keep it 'on the curve' for some max accel, you do have to pull to at least the high 6's or so. |
Mark Eberhardt (Me_k)
Member
Username: Me_k
Post Number: 462
Registered: 5-2002
| | Posted on Thursday, April 03, 2003 - 8:31 pm: | |
I probably should have been more clear when I wrote that. It really is only a general rule of thumb. As Mitch points out, the idea is to maximize the area under the HP curve, which means you probably do want to go a little past the HP peak. The problem with most engines is that the HP fall off pretty fast past the peak, so it is very hard to hit the exact spot that maximizes area for each separate gear and stay out of the nose drive section. It�s also pretty hard to remember a different point for each gear out on the track. By picking a spot you can remember easily, you will have the best luck getting it right every time. The peak HP point will be very close to the optimum most of the time, but is usually about 200 or 300 rpm low. It is usually worse to be a little past optimum than a little short because of the shape of the curve, but you know you�re probably shifting too soon if you end up below the torque peak. That�s where the rule comes from. If the gears are too far apart, you will end up both below the torque peak and above the hp peak, but that�s not the case with a 308. Hope this helps a little. |
BretM (Bretm)
Advanced Member
Username: Bretm
Post Number: 3361
Registered: 2-2001
| | Posted on Thursday, April 03, 2003 - 4:13 pm: | |
The 2Vs reach max HP at redline or thereabouts (7700rpm), the QVs reach max HP at 6800rpm. It would seem with the 2Vs that you would be best off throwing every shift near redline then regardless. The QVs is where it gets more interesting. |
Hans E. Hansen (4re_gt4)
Intermediate Member
Username: 4re_gt4
Post Number: 1028
Registered: 4-2002
| | Posted on Thursday, April 03, 2003 - 4:01 pm: | |
The "keep it between the torque peak and HP peak" rule of thumb is what is taught truck drivers.
When I went to a performance driving school years ago, we spent some time with complicated graphs derived from the engine torque curves and gear ratios. The gist is precisely what Mike's friend is getting at. As he mentions, if you shift too soon, you find yourself way too far down the power curve in the new gear. The later Callaway Twin Turbo Corvettes had little low end, as boost was formed only at high rpm. If you shifted at redline, you'd find yourself well below where boost would come in. So to have any reasonable power in the next gear, you'd have to rev beyond the redline - and also beyond the power peak. Big flaw in that setup, IMO. |
Chris F. (Chrisfromri)
New member
Username: Chrisfromri
Post Number: 28
Registered: 1-2003
| | Posted on Thursday, April 03, 2003 - 11:52 am: | |
Mitch,
I did the best I could do with a ruler on a little graph from a magazine article. The graph shows a very steep linear rise in horsepower peaking at just under 7000 RPM, and then falling off at a less steep slope.
The torque curve, however, is very flat with a smooth very gently rounded curve peaking at about 190 pounds-feet, and the scale is highly compressed (probably to make the curve look this way) -- obviously too much so to pull accurate numbers off of.
Does someone have tabular torque or horsepower data from an "accurate" dyno test?
I believe that we are talking about the 308 QV here, which has different torque/horsepower curves and also different final gear ratios, than the 308 2V.
Kind Regards, Chris |
Lawrence Coppari (Lawrence)
Member
Username: Lawrence
Post Number: 561
Registered: 4-2002
| | Posted on Thursday, April 03, 2003 - 11:05 am: | |
For anyone who is interested, the 5252 divisor comes from dividing 33000 by 2*pi. A horsepower is 33000 ft-lbs/min. The rpm must be changed to radians/minute. That's why the 2*pi enters the calculation. |
Mitch Alsup (Mitch_alsup)
Member
Username: Mitch_alsup
Post Number: 459
Registered: 4-2002
| | Posted on Thursday, April 03, 2003 - 10:50 am: | |
Cris: The data you give indicates that HP is still rising at 7500 RPMs. HP = TQ*RPM/5252
rpm...tq..hp
5000 190 181
5500 190 199
6000 185 211
6500 180 223
7000 175 233
7500 170 243
The white space cruncher makes it really hard to produce reasonable tabular data sets. |
Mitch Alsup (Mitch_alsup)
Member
Username: Mitch_alsup
Post Number: 458
Registered: 4-2002
| | Posted on Thursday, April 03, 2003 - 10:49 am: | |
Cris: The data you give indicates that HP is still rising at 7500 RPMs. HP = TQ*RPM/5252
tq hp
5000 190 181
5500 190 199
6000 185 211
6500 180 223
7000 175 233
7500 170 243 |
Mitch Alsup (Mitch_alsup)
Member
Username: Mitch_alsup
Post Number: 457
Registered: 4-2002
| | Posted on Thursday, April 03, 2003 - 10:44 am: | |
The car accelerates fastest when the area under the HP curve is maximized per shift. So, depending upon the shape of the HP curve and the max safe RPMs and the spread between the gears; you will always be shifting above the RPMs where max HP is achieved. |
Chris F. (Chrisfromri)
New member
Username: Chrisfromri
Post Number: 27
Registered: 1-2003
| | Posted on Thursday, April 03, 2003 - 10:39 am: | |
Mike,
From the Owners Manual for a US 308 QV the following gear ratios are listed: 1st 1:3.419; 2nd 1:2.353; 3rd 1:1.693; 4th 1:1.244; 5th 1:0.919. Also, the differential ring and pinion ratio is listed as 16/65.
There is no torque curve in the Owners Manual, but I found a small torque vs. horsepower graph in the Car & Driver review article of August 1983. It is a very flat torque curve, and using a ruler to interpolate I came up with the following approximate points: 5000 RPM/190 SAE net pounds-feet; 5500/190; 6000/185; 6500/180; 7000/175; 7500/170. Unfortunately, the graph is too small and coarse to provide greater detail and accuracy. Possibly someone has some detailed dyno numbers.
Kind Regards, Chris |
Mike Charness (Mcharness)
Member
Username: Mcharness
Post Number: 416
Registered: 8-2002
| | Posted on Thursday, April 03, 2003 - 8:23 am: | |
This thread started in "general" but is taking on a more technical aspect, so I thought I'd ask the question here.
Mark Eberhardt stated, "If your QV is stock, I think you'll find it goes faster if you shift at 6800 RPM. Performance is always achieved by keeping the engine [RPM] between peak torque (5000 carb, 5500 QV) and peak HP (7500 carb, 6800 QV)."
I find that a very interesting concept, so I asked a buddy who does real wheel-to-wheel racing and does race car customization about Mark Eb's statement. Below is his response... in general he agrees with Mark for the higher gears, but not for the lower gears. Does anyone have these numbers I can give him for a 308QV he's asking for or know where I can get them? There's no torque curve in my owners manual.
------------------------------------------
For max acceleration, the optimal shift rpm is a function of two things:
1) The torque curve of the engine. To calculate the shift point accurately, you need to know the engine torque at each 200 rpm increment from 5500 on up to the safe maximum redline of the engine
2) The gear ratios in the transmission
Each tranny gear ratio multiplies engine torque, and then passes that torque on to the rear axle. By maintaining as high as torque as possible at the rear axle, you will accelerate the car forward as fast as you can. Each time you upshift into a higher gear, the higher speed gear has a lower numerical gear ratio, so it multipies engine torque less, so you deliver less torque to the rear axle to accelerate the car.
Each gear ratio has a different spread or drop in rpm as you shift. For street transmissions, you will find they have a very low 1st gear to help launch the car with minimal clutch strain, then a fairly big drop in rpm as you shift to 2nd, then a closer rpm drop as you shift to 3rd, then a fairly small close drop to 4th, then the rpm drop to 5th can be small if they are looking for performance, or a large drop in rpm if they are looking for 5th gear economy hiway cruising mpg. For a race tranny like mine, where we do rolling starts on the race track, we run very, very high 1st gears, and try and minimize our rpm drops each time we shift gears.
In general, when you have big rpm drops like you do in a street tranny between 1st and 2nd gear, you should shift gears at max. safe engine redline, so that when the rpms drop as you engage 2nd gear, you have the max. possible torque delivered to the rear wheels. When you get to higher mph speeds, the 3rd to 4th shift is probably best to do at max. engine power rpm.
If you can come up with your engine torque vs rpm, and your tranny ratios, I can help you calculate your optimal shift points for each gear change. If you know the horsepower vs rpm for every step above 5500 rpm, I can calculate the torque from rpm and horsepower numbers.
|
|