What is the purpose of heel-and-toe downshifting?
For aggressive cornering, you need to get into the next gear in the middle of the turn so that you're prepared to exit the corner under hard throttle without having to take the time to shift. By using heel-and-toe, you can accomplish the rev-matched gear shift at the same time as you're braking hard into the corner. Doing two things at once saves time. Otherwise, you'd be on brake, off brake, shift, back on brake, corner, off brakes again, accelerate. This way, you're on brake, shift while still braking, blip throttle to rev-match while still braking, corner, off brakes, on throttle.
By virtue of rev-matching the downshift, you're also preserving the stability of the vehicle (no jerky shifting), meaning you can corner further toward the envelope of adhesion without needing to worry about breaking traction when the shift upsets the balance of the car.
You usually only need to *use* rev-matching for downshifting, but the concept is the same regardless of what gear you're coming from, what gear you're going to, and how fast you're going. The basic concept is that you need to figure out what your new engine RPM will be in the new gear, and make sure that the engine is at that speed before letting the clutch out in the new gear.
A common example of a rev-matched upshift is at the end of a quarter mile run. I don't know if anyone else does this, but I do. When you pass through the traps, you're at around 100-110mph at the very top of third gear (near redline). I immediately shift to 6th gear so that I'm not using compression braking by just jumping off of the throttle at 7000rpm in third gear. However, I can shift from third to sixth pretty quickly, so by the time the gear is in, the engine RPMs are only down to about, say, 5000rpm. Sixth gear is about 31.5 mph/krpm, so if I'm doing 110mph, divided by 31.5 mph/krpm, that means that my new engine speed will be about 3500rpm. If I were to jump off of the clutch as quickly as possible, the engine would be at 5000rpm, but the gearing would want the engine to be at 3500rpm, and so the car would lurch forward suddenly (lots of drivetrain stress!!!) as all of the "slack" is taken up by the transaxle, transfer case, driveshaft, rear differential, center differential, and hopefully mostly the tires. If I let the clutch out slowly, the clutch will spin to take up the "slack" between 5000rpm and 3500rpm, the drivetrain will be fine, but that's extra wear on the clutch. So what I do instead is wait for the revs to fall to 3500rpm, and then let the clutch out as quickly as possible. Result? No stress on any component of the drivetrain (since everything is "rev-matched"), and the clutch doesn't get any extra wear.
When rev-matching an upshift like that, you really can't do much to "help" the revs fall faster, except *maybe* double-clutch. I haven't tried this yet but intend to. I don't know if it will be any faster, though. That is, you could blast through the traps at 7000rpm in third gear, clutch in, move the stick to neutral, clutch out, revs fall more quickly, clutch in, move the stick to sixth gear, make sure you're rev-matched (blip if you let the revs fall too far), clutch out. It might be faster to just wait for the revs to fall on their own.
NOW... the more common case of rev-matching is for downshifting. Let's use your example below:
So if I'm going 25mph in 2nd and want to downshift to 1st for immediate throttle response I would need to bring the revs for what 25mph would be in 1st right?
Correct, although there's more to it than "immediate throttle response" - it also, in my opinion, will save wear on the drivetrain and clutch when executed properly. And, not to pick on your example, but 25mph is a little too high to bother downshifting into 1st gear - that would be almost 5000rpm, which is starting to get out of the power band. You'll probably get overall better acceleration by just mashing the throttle in second gear - you won't pull as hard initially, but you save yourself the wasted time shifting twice (2-->1, then 1-->2 just a moment later).
The exact values of the "constants" for each gear can be difficult to remember, so just remember my "approximation" instead: 5mph/krpm times the gear number. Specifically:
The "constant" tells you the mph/krpm in each gear. So, for example, if your current vehicle speed is 40mph, the approximation for each gear would be:
Note that the approximation isn't completely accurate (in first gear at 40mph, you're actually just under 7000rpm, because the constant is more like 6mph/krpm). However, the approximation is good enough for rev-matching, since you're not going to get the revs *exactly* where you want them to be anyway.
On my old '93 base model Stealth (SOHC 3.0L, 5-speed manual), the approximation was almost exactly correct for every gear. On my '95 R/T Turbo (6-speed), the constants are all slightly higher than the approximation - first gear is more like 6mph/krpm, second gear is more like 11mph/krpm, etc., all the way up to sixth gear which is more like 31.5mph/krpm.
Knowing the gear "constants" can also help you quickly decide what gear would be the best one to engage for peak acceleration at a certain speed. That is, for any given vehicle speed X, you can quickly do some mental math to decide what gear will put you closest to about 3500rpm (or whatever your car's "sweet spot" happens to be).
So, using the same example as above, if you're rolling along at 40mph in fourth gear when Mr. Stud in his Mustang 5.sl0w comes driving by, and he revs up and tries to race you from this rolling start at 40mph, you would know that downshifting to third would put you at about 2700 rpm (too low) whereas second gear would put you at 4000rpm - good portion of the power band.
let's say 25mph in 2nd is 2500rpm, and is 3500rpm in 1st.. when do I rev match? it wouldn't be before the shift 'cause that would shoot the rpms once clutch is pressed, right? can't imagine it being during the shift (too many changing variables), so is it after the shift before releasing the clutch?
You'll need a better imagination, then, because it *is* during the shift. :-) You should be jamming in the clutch, moving the shifter out of your old gear and into your new gear, and rev-matching (by "blipping" the throttle in most cases) all at roughly the same time.
In the case of the original discussion, downshifting into first while rolling, you won't even be able to engage the shifter into first (even with the clutch depressed) unless you already have the engine at the appropriate speed (rev-matched). So if Mr. Stud in his Mustang finally catches up to you at the next stoplight, and you're rolling at 15mph in third gear while he's coming up behind you at about 40mph, and the light suddenly turns green in front of you, you:
That might sound like a lot to keep track of and a lot to do, but a good portion of it should happen simultaneously (or nearly so) and the entire procedure should take less than one second.
Once you start to do this, it will become second nature and you won't have to *think* about it anymore; it will just *happen naturally* as part of your normal driving routine. That includes memorizing the gear constants - once you know them, you don't have to *think* about them anymore, and you don't have to waste time doing math. You'll just subconsciously "feel" what the correct gear and engine speed is for any particular vehicle speed.
And, once you perfect basic rev-matching under all conditions (downshifting, upshifting, it even plays a role in drag strip launches), then you get to graduate to really fun stuff, like how to rev-match a downshift in a corner while also heel-and-toe braking at the same time.
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