Let's examine the Virago's valve timing in detail.

We'll start with the basic characteristics of this four-stroke engine.

The Virago engine is a four-stroke 'Otto cycle' engine.

(Trivia: Nikolaus Otto demonstrated this kind of engine in 1876. (Wikipedia article)

Four strokes of the piston (up-to-down, down-to-up, up-to-down, and down-to-up) are required for each complete engine cycle.

The four strokes are (in order): intake, compression, power, and exhaust.

Only the power stroke releases power.

The major parts of our four-stroke engine (simplified):

• Piston - moves up and down within an enclosing cylinder
• Crankshaft - connected to the piston (via a rod)
• Intake valve - opens to allow fuel/air mixture into the cylinder (every other time the piston moves down)
• Exhaust valve - opens to allow exhaust gas out of the cylinder (every other time the piston moves up)
• Spark plug - ignites the fuel/air mixture (when the piston is up)
• Camshaft - opens/closes the valves (driven by the crankshaft)

The Virago has two cylinders that share a single crankshaft.

We'll start with just the piston and crankshaft, and add additional components as we go along.

A rod with bushings on each end connects the piston and crankshaft.

If we turn the crankshaft, the piston goes up and down.

Let's describe the crankshaft and piston movement:

The piston will move all the way through the cylinder (all the way from one end to the other), for each half-turn of the crankshaft.

If we turn the crankshaft one whole turn, we get two piston strokes; two revolutions gives us four strokes - and so on.

1. At the beginning of the first stroke, the piston is at the top of its cylinder: the crankshaft is at 0 degrees.
   

   
   During the first stroke, the piston moves all the way to the bottom of its cylinder as the crankshaft rotates one-half turn, or 180 degrees.

2. At the beginning of the second stroke, the piston is at the bottom of its cylinder: the crankshaft is at 180 degrees.
   

   
   During the second stroke, the piston goes all the way to the top of its cylinder as the crankshaft rotates another one-half turn, or from 180 to 360 (or 0) degrees.

3. At the beginning of the third stroke, the piston is again at the top of its cylinder.
   

   
   During the third stroke, the piston again travels from the top to the bottom of its cylinder, from 0 to 180 degrees (or from 360 to 540 degrees, if we include the previous 360 degrees.)

4. At the beginning of the fourth stroke, the piston is again at the bottom of its cylinder.
   

   
   During the fourth stroke, the piston again travels from the bottom to the top of its cylinder, from 180 to 360 degrees (or 540 to 720 degrees, counting the previous 360 degrees).

About degrees:

It's common to measure a shaft's rotation in degrees. A complete revolution is 360 degrees; a half-revolution is 180 degrees; a quarter-revolution is 90 degrees, two whole revolutions is 720 degrees, and so on.

Trivia: Apparently, 360 was chosen because there are about 360 days in a year, so celestial stuff appears to move about one degree per day. (Wikipedia article)

Now, let's add a camshaft, two valves and a spark.

The camshaft's job is to open and close the intake and exhaust valves.

The camshaft is geared to the crankshaft so that we have to turn the crankshaft two whole turns to make the camshaft turn one whole turn.

Let's describe the four strokes again:

1. The intake stroke:
   • At the beginning of this stroke, the piston is at the top of its cylinder, and the crankshaft is at 0 degrees.

     The intake valve is opening.

   • During this stroke, the piston moves from the top to the bottom of its cylinder as the intake valve is gradually opened fully, then gradually closed.

   • At the end of this stroke, the cylinder is filled with an air/fuel mixture.

     The intake valve is (almost) fully closed.

2. The compression stroke:
   • At the beginning of this stroke, the piston is at the bottom of its cylinder, and the crankshaft is at 180 degrees.

   • During this stroke, the piston moves from the bottom to the top of its cylinder, compressing the air/fuel mixture.

     Both valves are closed.

   • At the end of this stroke, the air/fuel mixture is compressed.

3. The power stroke:
   • At the beginning of this stroke, the piston is at the top of its cylinder: the crankshaft is at 0 (360) degrees.

     Both valves remain closed.

     A spark (from the coil attached to the spark plug) ignites the air/fuel mixture, rapidly increasing the gas pressure in the cylinder.

   • During this stroke, the piston moves from the top to the bottom of its cylinder, pushed by the pressure of the rapidly-expanding gases.

   • At the end of this stroke, the exhaust gases have expanded.

4. The exhaust stroke:
   • At the beginning of this stroke, the piston is at the bottom of its cylinder: the crankshaft is at 180 (540) degrees.

     The exhaust valve is opening.

   • During this stroke, the piston moves from the bottom to the top of its cylinder as the exhaust valve is gradually opened fully, then gradually closed.

   • At the end of this stroke, the exhaust valve is (almost) fully closed.

Simplifications:

• The obvious way to figure out when to generate the spark is by camshaft position.

  Instead, some designers use a crankshaft position sensor, so spark timing is unaffected by any slop in camshaft timing.

  As a side effect (because the crankshaft turns twice as fast as the camshaft), a second spark occurs around the start of the intake stroke, which doesn't affect the uncompressed mostly-exhaust gases.

Now, let's describe the four strokes again, in three times more detail:

Here's one cylinder, every 60 crankshaft degrees (or 30 camshaft degrees):

We'll (arbitrarily) measure the camshaft position from the start of the POWER stroke, not the intake stroke.

We do this because the timing-critical stuff happens when the compressed air/fuel mixture is ignited by the spark, not when the intake cycle begins.

"BDC" = Bottom Dead Center
"TDC" = Top Dead Center

Cycles:
intake/
compression
power
exhaust

Simplifications:

• The spark is actually applied a few cam degrees before TDC of the power stroke. The air/fuel mixture doesn't all burn instantly, so we start the burn a little earlier.

• The intake valve actually begins opening a few cam degrees before the exhaust valve is completely closed. (Air has mass.)

Now, let's examine this twice the detail, and with two cylinders, arranged like a Virago.

• We'll add a second cylinder, also pointing towards the crankshaft, placed 75 degrees in front of the first cylinder.
  
• We'll use the same crankshaft throw for both connecting rods.
  • One piston will be 75 crankshaft degrees ahead of the other.
    
  • We'll connect the rods to the crankshaft side-by-side, with the rear cylinder's rod on the left.
    
  • We'll also stagger the rear cylinder slightly to the left of the front cylinder, by the same distance that its rod is staggered.
    (We won't use Harley-style forked-and-tongued rods.)

• We'll also separate the firings by 285 [crankshaft] degrees (rather than just 75 [crankshaft] degrees), to better distribute the power.

Notes about this table:

• There are two camshafts, and one flywheel (the alternator rotor).
  
• We'll list timing degrees for each camshaft/crankshaft/stroke.

• cam-1 (rear) rotates CCW (viewed from left)(same side as its sprocket).
  
• cam-2 (front) rotates CW (viewed from right)(same side as its sprocket).
  
• crankshaft rotates CW (viewed from left)(same side as its timing window).
  
• piston strokes are: intake, compression, POWER, and exhaust.
  
• We'll measure cam degree angles from the start of the associated POWER stroke, not the intake stroke.
  
• CW = clockwise; CCW = counterclockwise.

Now, let's examine the timing gears and sprockets.

The camshaft makes one complete revolution for every two crankshaft revolutions (and every four piston strokes).

The total reduction, from crankshaft to camshaft, is 2:1.

• We can verify this by counting the meshing teeth and sprockets between the crankshaft and camshaft.
  
• The crankshaft is fixed to the timing drive gear.
  
• The timing drive gear turns the timing driven gear at a 10:7 reduction ratio.
  • The timing drive gear (on the crankshaft) has 35 teeth.
    
  • The timing driven gear has 50 teeth.
    
  • This yields a reduction of 50:35 (or 10:7)(or 70%).
    
  • For every 350 teeth, the drive gear revolves 10 times, and the driven gear revolves 7 times.)

• The timing driven gear is fixed to the camshaft drive sprocket.
  
• The camshaft drive sprocket turns the camshaft driven sprocket at a 7:5 reduction ratio.
  • The camshaft drive sprocket has 20 teeth.
    
  • The camshaft driven sprocket has 28 teeth.
    
  • This yields a reduction of 28:20 (or 7:5)(or about 71.4%).
    
  • For every 140 teeth, the drive sprocket revolves 7 times, and the driven sprocket revolves 5 times.

• The camshaft driven sprocket is fixed to the camshaft.
  
• So, these reductions are 10:7 followed by 7:5, which is 10:5, which is 2:1.

How is cam timing affected by each timing gear tooth and/or sprocket?

One gear tooth changes cam timing by about 5.14 degrees.
One sprocket changes cam timing by about 12.86 degrees.
Using both, we can change cam timing by steps of about 2.57 degrees.

Here's the math:

• We'll use units of 1/140 of a camshaft revolution (about 2.57 cam degrees).
  • (The camshaft drive sprocket has 20 teeth.)
    
  • (The camshaft driven sprocket has 28 teeth.)
    
  • Let's factor.
    
  • 20 = 2 * 2 * 5
    
  • 28 = 2 * 2 * 7
    
  • 140 = 2 * 2 * 5 * 7

• One camshaft driven sprocket tooth is 5/140 cam revolution, about 12.86 cam degrees.
  • (There are 360 degrees in a circle.)
    
  • (The camshaft driven sprocket has 28 teeth.)
    
  • = 360 * 1/28
    
  • = 360 * 5/140
    
  • ~= 12.857 cam degrees per camshaft driven sprocket.

• One timing driven gear tooth is 2/140 cam rotation, about 5.14 cam degrees.
  • (There are 360 degrees in a circle.)
    
  • (The timing driven gear has 50 teeth.)
    
  • (The camshaft drive/driven sprocket reduction is 7:5, or 5/7.)
    
  • = 360 * 1/50 * 5/7
    
  • = 360 * 5/350
    
  • = 360 * 1/70
    
  • = 360 * 2/140
    
  • ~= 5.142 cam degrees per timing driven gear tooth.

• These may be combined:
  • Two sprockets are exactly equivalent to five teeth, and yields 10/140 cam revolutions (about 25.71 cam degrees).

  • One sprocket is equivalent to 2.5 teeth, and yields 5/140 cam revolutions (about 12.86 cam degrees).

  • Two timing driven gear teeth yields 4/140 cam rotation (about 10.28 cam degrees).

  • One timing driven gear tooth, and one opposed camshaft driven sprocket tooth,
    yields 3/140 cam rotation (about 7.71 cam degrees).
    • = 360 * (5 - 2)/140
      
    • = 360 * 3/140
      
    • ~= 7.714 cam degrees

  • A half-sprocket is equivalent to 1.25 teeth, 2.5/140 cam revolutions (about 6.43 degrees), (but you can't get there from here;-).

  • One timing driven gear tooth yields 2/140 cam rotation (about 5.142 cam degrees).

  • One camshaft driven sprocket, and two opposed camshaft driven teeth,
    yields 1/140 cam rotation (about 2.57 cam degrees).
    • = 360 * (5 - 2 - 2)/140
      
    • = 360 * 1/140
      
    • ~= 2.5714 cam degrees

Our stretched camshaft chains appear to have retarded our camshaft timing by slightly less than a half-sprocket, or about 5 cam degrees.

Any cam lobe wear would also retard timing a tiny amount more.

Advancing each camshaft driven gear by one tooth (about 5.142 cam degrees) should compensate for this timing change. Theoretically.

Disclaimer:

• The proper way to address a worn-out chain is to replace it, along with any excessively-worn chain guides and sprockets.
  
• A worn-out chain may eventually rub against its enclosure, slip a tooth, or even break.
  
• A broken chain on an interference engine is A Bad Thing. (The valves get in the way of the pistons!)
  
• We haven't tried this on our engine because we didn't do the math until after reinstalling the engine.
  
• I am not a mechanical engineer. I may be wrong. Your mileage may vary.