Refresh my calculus

[J-Madd]

Regardless of the ignition system employed, the spark plug must fire at the correct

time if good power is to be made and engine damage avoided. Some two-strokes are

timed to spark at 2mm before TDC, others at anywhere from 0.4mm to 4mm.

Probably you are wondering why the difference? Well, first, the length of the engine's

stroke will affect the amount of advance required. A short stroke engine with 2mm

advance will have considerably more advance measured in degrees of crankshaft

rotation than a long stroke engine with spark timing of 2mm before TDC. For

example, a 125cc engine with a stroke of 60mm and 2mm ignition advance has 18.8

[BellicoseBanshee]

Someone has been reading the A. Graham Bell book...

[BellicoseBanshee]

I think the answer lies in the definition of cosine:

 

cos θ = (X / r)

 

Where:

θ = angle in degrees

X = adjacent side of triangle contained within the unit circle

r = 1, radius of the unit circle

 

Since we are using the unit circle where r = 1:

 

cos θ = X

 

The formula states: A = cos [(P^2+R^2-L^2)/2PR]

 

If you consider the formula for the inverse cosine, cos^-1, it states:

 

cos^-1 X = θ

 

If the formula is written: A = cos^-1 [(P^2+R^2-L^2)/2PR], the math works out.

 

cos^-1 (8404/8880) = 18.8

[Bansh-eman]

I think the answer lies in the definition of cosine:

 

cos θ = (X / r)

 

Where:

θ = angle in degrees

X = adjacent side of triangle contained within the unit circle

r = 1, radius of the unit circle

 

Since we are using the unit circle where r = 1:

 

cos θ = X

 

The formula states: A = cos [(P^2+R^2-L^2)/2PR]

 

If you consider the formula for the inverse cosine, cos^-1, it states:

 

cos^-1 X = θ

 

If the formula is written: A = cos^-1 [(P^2+R^2-L^2)/2PR], the math works out.

 

cos^-1 (8404/8880) = 18.8

[flyhighprerunner]

I think the answer lies in the definition of cosine:

 

cos θ = (X / r)

 

Where:

θ = angle in degrees

X = adjacent side of triangle contained within the unit circle

r = 1, radius of the unit circle

 

Since we are using the unit circle where r = 1:

 

cos θ = X

 

The formula states: A = cos [(P^2+R^2-L^2)/2PR]

 

If you consider the formula for the inverse cosine, cos^-1, it states:

 

cos^-1 X = θ

 

If the formula is written: A = cos^-1 [(P^2+R^2-L^2)/2PR], the math works out.

 

cos^-1 (8404/8880) = 18.8

[BellicoseBanshee]

Holy shit, I thought you were a math nerd when you helped me with my basic college algebra, but your nerdiness just went to a whole new level in my book!!

I just quickly glanced it, looks pretty damn good!!!! I would have gotten way to pissed of my CPU calculator and did it on the TI but whatever you did it bad ass!

I am assuming you are referring to a graphing calculator. The fact that all the values can be stored makes the calculating process easier. I am old school, I still prefer to work problems with pencil, paper, and simple scientific calculator whenever possible...

[BellicoseBanshee]

J-Madd, it looks like the same applies to the valve timing formula as well...

 

A = cos [(T^2 + R^2 - L^2)/(2 X R X T)]

 

Should be: A = cos^-1 [(T^2 + R^2 - L^2)/(2 X R X T)]

 

where:

R = stroke divided by 2 in mm

L = con rod length center to center in mm

C = deck clearance in mm

E = distance from the top of the barrel to the piston at the instant of inlet opening or closing

T = R + L + C - E

 

For:

R = 27mm

L = 110mm

C = 1.8mm

E = 44.7mm (valve opening) 31.9mm (valve closing)

T = 94.1 (valve opening) and 106.9 (valve closing)

 

Valve opening:

 

A = cos^-1 (-2516.19/5081.4)

A = cos^-1 (-0.49518)

A = 119.7

[Bansh-eman]

Does anyone else think that all of this looks like Chinese?

[dragbanshee]

J-Madd, it looks like the same applies to the valve timing formula as well...

 

A = cos [(T^2 + R^2 - L^2)/(2 X R X T)]

 

Should be: A = cos^-1 [(T^2 + R^2 - L^2)/(2 X R X T)]

 

where:

R = stroke divided by 2 in mm

L = con rod length center to center in mm

C = deck clearance in mm

E = distance from the top of the barrel to the piston at the instant of inlet opening or closing

T = R + L + C - E

 

For:

R = 27mm

L = 110mm

C = 1.8mm

E = 44.7mm (valve opening) 31.9mm (valve closing)

T = 94.1 (valve opening) and 106.9 (valve closing)

 

Valve opening:

 

A = cos^-1 (-2516.19/5081.4)

A = cos^-1 (-0.49518)

A = 119.7

[turbostang]

Got blurry vison and a headach reading this thread.

[BellicoseBanshee]

The formula to convert degrees to mm before TDC is correct:

 

T = L + R X (I - cos A) - [L^2 - (R X sin A)^2]^0.5

 

The formula for exhaust duration should be:

 

D = (180 - cos^-1 [(T^2 + R^2 - L^2)/(2 X R xT)]) X 2

or

D = 360 - 2cos^-1 [(T^2 + R^2 - L^2)/(2 X R xT)]

 

The formula for inlet duration should be:

 

D = (cos^-1 [(P^2 + R^2 - L^2)/(2 X P X R)]) X 2

or

D = 2cos^-1 [(P^2 + R^2 - L^2)/(2 X P X R)]

 

When using the formulas, simply remember that: the cosine of an angle is a number and the inverse cosine of a number is an angle, provided the numbers and angles fall within the range and domain of each function...

 

:beer:

 

And just a reminder for the formula in the exhaust chapter: cot = 1/tan :thumbsup:

[05.Banshee.SE]

Someone has been reading the A. Graham Bell book...

 

I thought it looked familiar. :biggrin:

[J-Madd]

The formula to convert degrees to mm before TDC is correct:

 

T = L + R X (I - cos A) - [L^2 - (R X sin A)^2]^0.5

 

The formula for exhaust duration should be:

 

D = (180 - cos^-1 [(T^2 + R^2 - L^2)/(2 X R xT)]) X 2

or

D = 360 - 2cos^-1 [(T^2 + R^2 - L^2)/(2 X R xT)]

 

The formula for inlet duration should be:

 

D = (cos^-1 [(P^2 + R^2 - L^2)/(2 X P X R)]) X 2

or

D = 2cos^-1 [(P^2 + R^2 - L^2)/(2 X P X R)]

 

When using the formulas, simply remember that: the cosine of an angle is a number and the inverse cosine of a number is an angle, provided the numbers and angles fall within the range and domain of each function...

 

:beer:

 

And just a reminder for the formula in the exhaust chapter: cot = 1/tan :thumbsup:

 

 

 

Thanks all.

 

 

But why does he list the formula as Cos instead of Cos^-1 in the book??

 

 

 

EDIT: Note that the stupid CPU calculator has a box to check to get an inverse function. Just figured that out, and that fixes everything in the calculation.

[J-Madd]

Alright...I worked out the formula for my stock stroke Cub with the timing advanced 2mm and get 16.4*. This is less than the stock timing of 17*, therefore I need to advance it 8 or so more degrees to put it where it was with the stock cdi and timing plate at +8, correct?

 

Or does the PVL ignition advance the timing?? Pretty sure it has a built in retard curve, not sure about the advance....I guess I'll check Penton's web site. Either way, the damn thing took a crap, I think. I was in the staging lane for test and tune running fine, then got to the front of the line and the right side started detonating, almost blowing the pipe off. Never got to run it. Gonna test the coils and get a better ground (remove powdercoat) and see if that fixes it.

[BellicoseBanshee]

But why does he list the formula as Cos instead of Cos^-1 in the book?

Well, I was wondering that myself. I am more surprised that the those errors, and some grammitical errors as well, made it to the second edition. Oh well, it is still a great source of information...