Adjustable Vacuum Advance And HEI Distributor Recurve
Here is the distributor.
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As engine speed increases, your ignition timing must advance. Why? Intake charge (fuel air mixture) has momentum and mass. As engine speed increases, you need to spark the mixture sooner. This "times" the combustion so that the flame is more fully propagated across the combustion chamber as the piston reaches Top Dead Center.

If this happens too soon (i.e. the ignition is too far advanced) your engine will knock and ping. This is called predetonation, and it can cause engine damage. Major Engine Damage.

If this even happens too late (i.e. the ignition is too far retarded, as in the stock HEI curve) the piston will already be traveling down when the peak combustion takes place. This results in a loss of power and higher exhaust temperatures.

If none of that makes sense, it's okay. I probably got it wrong anyway.

But know this: Stock HEI C-3 Vettes aren't running enough ignition advance. It's been proven, time and again, weekend after weekend, day in and day out, that the small block Chevy will make more power with 34-36 degrees total mechanical advance, than with less. Stock HEI units only run 26-27 degrees.

So if you want a modification that is inexpensive yet very effective (seat of the pants difference), adjust your advance curve.
Remove the wires.  Mark them first!
Remove the spark plug wires and the distributor cap. Make sure you mark the wires first! Remember the firing order is 18436572. On an HEI car, the Number 1 plug terminal should be positioned around the same place you see it in this picture and the one above. A flat head screwdriver can be used on the 4 screws. A 180 degree turn is required of each screw, in order for the distributor cap tab to clear the body of the distributor.
Remove wires, cap, and then the rotor.
Remove the spark plug wires, distributor cap, and then the rotor. Here, you see the rotor. It is removed by loosening two phillips head screws.
Remove these screws.
Remove the screws.
Here are your advance springs...
Here you see the advance springs. They are attached to posts, which are, in turn, attached to the advance weights. The weights do not move independently of each other. Their movement is connected via the springs. Because of this, when you buy new advance springs, you can use any combination to achieve the advance you are looking for. Here, I have replaced a blue spring with a silver spring.

According to the instructions with my kit, the blue springs are the least aggressive. The silver spring is one step up. This means, with a combination of silver and blue, I'll have more centrifugal advance than with two blue springs.

Watch the movement of the weights, and you can see why it's called centrifugal advance. As the distributor shaft spins, it spins the weight/spring assembly. The weights are pulled out with the centrifugal force created. This causes the ignition to advance. The springs resist this force. The less the springs resist, the greater the centrifugal ignition advance.

The springs are easily removed. I use my fingers and a gentle twist to unseat the spring end. Then, I install a new spring.

While you're in here, it's a good idea to check the overall movement of the spring/weight assembly. The movement should be smooth, with no hang ups. If the assembly does not move smoothly, a little light oil may be needed. In more severe cases, you may need to replace the weights. These weights are provided with some advance kits.

I bought a kit from Summit, but found the weights to be of substandard quality, compared to the weights that were already installed.
Timing light.
Once the springs are in, you'll have to put it all back together, and check out the results. Once back together, start the car. Then pull out your timing light. Here is my Sears timing light. Because the battery in C-3's is behind the seats, accessing power for the timing light, is difficult. So I use a motorcycle battery. This makes it all very easy.
Attach to the number one spark plug wire.
Connect the timing light lead to the number 1 spark plug wire. This is the spark plug wire that is at the front left side of the engine. Be sure the timing light clamp is securely fastened around the spark plug wire. If it's not, it won't get a signal, and will not light.
Disconnect the vacuum advance.
Before checking your timing, disconnect and plug the vacuum hose that goes to the vacuum advance cannister. The cannister is the silver cylinder attached to your distributor.
Bring up the revs, aim the light, watch the numbers advance.
Start your car and aim the timing light at the timing tab on your harmonic balancer. This can be seen just forward and below your alternator.

Pull the trigger on the light, and you'll see your initial number. It should be around 10-12 degrees. If it's not, twist the distributor clockwise to retard the ignition (if you're higher than 10-12 degrees), or twist it counter clockwise to advance the timing.

Next, rev the engine and aim the light again. Watch the numbers on the balancer increase with the revs. By 2700 to 3000 RPM, your full advance of 34-36 degrees should be in, without pinging or detonation of any kind. If you experience detonation or pinging, you'll need to swap in a tighter spring.

My timing light does not have an advance on it. But my car has timing marks all around the harmonic balancer. This makes seeing my advance easy. Your balancer will most likely not have the marks all around it. So you'll want to pick up an advance light. To use it, dial in the advance you're looking for, and then look for zero on the balancer.

All balancers will have a zero on them. If you can't read it, take some mineral spirits and wipe down the balancer. This will help the readability. You can also paint a mark on it. Also, Lar's paper, found on Corvettefaq.com, explains how to degree your balancer using a tape measure.

In the picture above, it's exagerrated, but you can see the 36 degees coming in full. The next step, is to actually drive the car, under different conditions, to listen for load. This is very important, because of the reasons explained above. You may not hear anything in the driveway, because revving the engine presents a light load. But driving, especially up hill, or in hot weather, is another story.
Installing an Adjustable Vacuum Advance Cannister
Vacuum Cannister
Here is an adjustable vacuum advance cannister, already installed. The old cannister and the new one are both attached with two flat head screws, seen in this picture.

This is truly a bolt-off/bolt-on upgrade. The only difference with the adjustable cannister, is the oblong shaped metal disc I'm pointing to in the picture. This disk adjusts the maximum amount of vacuum advance that is possible. Rotate it counter clockwise (it's notched, each notch represents a different level of advance)to decrease the amount. Rotate it clockwise to increase the maximum amount.

Keep in mind, as you adjust the disc, you'll affect your base timing. So with each adjustment, make sure you double check the base and adjust as necessary.

Also, make sure your flat head screws are tight, after each adjustment.

Your adjustable advance cannister will also come with an allen wrench which is stuck into the opening of the cannister. Start off with the allen wrench turned clockwise all the way until it stops. This is your maximum advance curve, which means your vacuum advance will come in fast and furious. Drive the car. If it buck at part throttle or on the freeway while cruising, turn the allen wrench one full turn counterclockwise. This will retard the vacuum advance.

Then drive the car again. If the car is fine, you're done. If not, adjust accordingly until you have it all smoothed out.

Before buttoning up your distributor for the "final" time, inspect the rotor and cap. If any damage is evident, replace the parts.