Two-stroke Engine Formulas

2-Stroke Engine Formulas

(most applies to gas as well)

·      Engine Tuning and Diagnostic Formulas

·      Getting to Know Your Engine

·      Using What We Have Learned

·      Modifying Your Engine

·      The Tuned Pipe

·      Expansion Chambers According to Blair

·     Carburetors

Engine Tuning and Diagnostic Formulas

Specific Power of any Engine                                        SP (in hp/liter) = Horsepower / Displacement (in liters)

Predicting Power                                                            BHP = PLAN/33,000

  P is brake mean effective pressure, in PSI

   L is piston stroke, in feet

   A is the area of one piston, in square inches

   N is the number of power strokes per minute

Brake Mean Effective Pressure (BMEP)                   2-Stroke BMEP = (HP x 6500)/(L x RPM)

   L = Displacement in Liters  i.e., 80 cc = .08 Liters

   1 ci. = 16.39 cc

Piston Speed                                                                     Cm = .166 x L x N

   Cm is mean piston speed, in feet per minute

   L is stroke, in inches

   N is crankshaft speed, in RPM

Piston Acceleration                                                        Gmax = ((N² x L)/2189) x (1 + 1/(2A))

   Gmax is maximum piston acceleration, in feet per second squared

   N is crankshaft speed, in RPM

   L is stroke, in inches

   A is the ratio of connecting rod length, between centers, to  stroke

Piston Stroke Motion                                                     S = R cos X + L cos Z or sin X = R/L sin Z

   S= the distance piston wrist pin is from center of crankshaft

   R = the radius of the crankshaft wrist pin

   L = the length of the connecting rod

   X = the angle of the wrist pin

   Z = the angle of the  connecting rod

Piston Travel vs. Crank Rotation                                 d = ((S/2) + L) - (S/2 cos X) - L sin[cos-1 (S/2L sin X)]

   S = Stroke (mm)

   L = Connecting Rod Length (mm)                            Note: (L) Rod Length is usually 2 times the (S) Stroke

   X = Crank Angle Before or After TDC (deg)

 For Spreadsheets and some Calculators         HT = (r + c) - (r cos (a)) - SQRT(c² - (r sin (a))²)

      r = s/2

     dtor = PI/180

     a = d x dtor

     HT   = The height of piston

     r    = The stroke divided by 2

     c    = The rod length

     a    = The crank angle in radians

     d    = The crank angle in degrees

     dtor = Degrees to Radians

Port Open Time                                                         T = ( 60/N ) x ( Z/360 ) or T = Z/( N x 6)

  T is time, in seconds

   N is crankshaft speed, in RPM

   Z is port open duration, in degrees

Compression Ratio                                                         CR = ( V1 + V2 ) /  V2

   CR is compression ratio

   V1 is cylinder volume at exhaust closing

   V2 is combustion chamber volume

Exhaust Systems Tuned Length                                    Lt = (Eo x Vs) /  N

   Lt is the tuned length, in inches

   Eo is the exhaust-open period, in degrees

   Vs is wave speed in feet per second (1700 ft/sec at sea level)

   N is crankshaft speed, in RPM

  Length of Curved Pipe                                                 L = R x .01745 x Z

   L is length

   R is radius of the pipe bend

   Z is the angle of the bend

 Diffuser Proportions                                               D2 = SQRT( D1² x 6.25 )

      D2 is the diffuser outlet diameter

      D1 is the diffuser inlet diameter

      6.25 is the outlet/inlet ratio constant

 Baffle Cones                                                              Lr = Le/2

    Lr is mean point of the reflection inside the baffle cone

      Le is the length of the baffle cone

Rotary Valve Timing

The Rotor Valve timing sets the low end power.  Insure a snug fit  and flat surfaces between the rotor and backplate. The point of opening for a rotary valve is best     established at the  point of transfer port closing if you want a very broad range of   power.  Maximum power is obtained by opening the intake port  somewhat earlier: from 130 to 145 degrees before top dead center (BTDC).

Exhaust Port Timing

Sets the RPM range of the engine.  Lower the Exhaust timing for low end power and raise the timing for high end power.The higher the Exhaust timing the higher the RPM band.

Carburetor Throttle Bore Diameter                          D = K x SQRT( C x N )

    D is throttle bore diameter, in millimeters

    K is a constant ( approx. 0.65 to 0.9, derive from existing carburetor bore)

    C is cylinder displacement, in liters

    N is RPM at peak power

Getting To Know Your Engine

So now that we have the formulas, what do we do with them? Well we first have to understand our engines. Let's take a look at a typical high performance engine. This is an exploded view of a Rossi .40 rear rotor engine that I borrowed from Martin Hepperle's "Airfoils" web site.

We want to concentrate mainly on the sleeve and it's ports. They are the exhaust port, usually the largest port in the sleeve and allows the burned gases to escape from the engine, the transfer port, usually 2 ports located at 90 degrees to the exhaust port and transfers fresh fuel from the crankcase to the sleeve, and the boost port, 1 or 2 ports located 180 degrees from the exhaust and helps evacuate the exhaust gases and supply fresh fuel.

The first thing you should do with a new engine is take it completely apart and clean any burrs or metal shavings from inside the engine. Pay close attention, take good notes and make sketches as you disassemble the engine. It is real easy, in some cases, to put things like pistons and rotary valves in backwards or upside down. I usually mark the parts with a marker or an awl to identify positions. Remove the sleeve from the case and disassemble the piston and connecting rod. You may need to heat the case in order to remove the sleeve. Use a propane torch or place in the oven at 350 degrees and evenly heat the case until the sleeve can be removed. Wash all parts in warm soapy water with a tooth brush or any other soft bristled brush and dry. If you have an air compressor you can blow the parts dry or use a blow dryer. Spray the front bearings with WD40 (WD stands for Water Displacement) as soon as you have dried the front case assembly to prevent corrosion.

Now we will fit the rotor valve to the backplate. Place the pin into the rotor valve and the backplate. Place a .0015 or .002 feeler gauge or shim stock between the rotor and backplate on one side only and while holding these parts together firmly, tighten the set screw. Lubricate this assembly with WD40 and set aside for final assembly. This process should be performed at a minimum of twice a season and lap if necessary as this fit is critical to good performance. The rotor valve is the heart of the engine.

At this point it is time to take careful and precise measurements of your engine using a micrometer. Measure the distance between connecting rod bearing centers by either measuring between the top of one bearing to the top of the other or measure the distance from inside to inside edge of each bearing and subtract from the outside to outside edge measurement. Measure the piston height from the crown (top) to the center of the wrist pin and from the center of the wrist pin to the skirt (bottom). Measure from crown to skirt and compare measurements for accuracy of the previous measurement. Measure the thickness of the head gasket. Measure the depth of the head from the squishband to the bottom of the head. Measure the head bowl depth and width. Now roll up a piece of paper and place it inside the sleeve. Carefully trace the port openings to the paper making sure that the paper does not move. Mark the top and bottom of the sleeve. Remove the paper and you should have a sketch of the port relationships to use later for timing measurements.

Lap the sleeve to the case so that the sleeve can be easily installed and removed without heating. Use a lapping compound made especially for aluminum or "non-imbedded granet". Again wash with warm soapy water and a soft brush at least three times and dry. Reassemble the engine with the exception of the head and head gasket using a torque screw driver if available. If not be careful not to overtighten the screws. 12 in-lb of torque is all you need for most all engines and that isn't very much compared to what you can exert with a 5 inch screw or allen driver. Use your notes you made previously to make sure you reassemble the engine correctly. After reassembly turn the crankshaft slowly and feel for rough spots or sticking. If this occurs dissassemble, clean, lubricate, reassemble and test again until there are no rough spots or sticking. Even new bearings may need to be replaced.

The following measurements are the most critical of all. You may want to make an engine stand to aid in performing these measurements. Equipment required to perform these measurements are: high intensity light or small flashlight and a good set of calipers/micrometers. I use a digital caliper made in Switzerland by General Tool and cost about $55. They are accurate to within .001 inch and measure in inches or millimeters. Not as accurate as I would like, but within my price range.

These are the measurements you want to make:

Top of sleeve (TOS) to top of piston (TOP) at top dead center (TDC)

TOS to TOP at bottom dead center (BDC)

TOS to top of transfer port

TOS to bottom of transfer port or BDC ***

Height of transfer port

Width of transfer port

TOS to top of boost port

TOS to bottom of boost port or BDC  ***

Height of boost port

Width of boost port

TOS to top of exhaust port

TOS to bottom of exhaust port or BDC ***

Height of exhaust port

Width of exhaust port

*** Note: The bottom of these ports measured against the piston top may or may not be at BDC. It is highly unlikely that they are above the piston top, but they may be below BDC in which case you write down BDC measurement.

Turn the crankshaft in the counterclockwise direction until the rotor valve just starts to open and measure from TOS to TOP. Turn crankshaft clockwise until rotor valve is just closed and measure TOS to TOP. Install the head and gasket and torque it down.

Congratulations!!! You have just performed the first steps in knowing your engine from the inside. Now go have some fun and break it in !!!!!!! Run at least 3 tanks of fuel through it running on the rich side with 25% nitro fuel. Then use the fuel you plan on using for at least another 2 tanks full.

Using What We Have Learned

We have learned the formulas, disassembled, cleaned, lubricated, assembled and measured our engines and have properly broken them in. Now what? Well I'm affraid we have to repeat those procedures again. You see while breaking in that engine, you got it dirty and loosened up some parts. So get to the bench and start over from scratch including those measurements. Look closely at the parts, don't just wash them. Any scratches or cracks? Metal shavings? Having fun yet? No this is not as much fun as flying or driving, but you put in 3-4 hours at the field, now it's time to put 3-4 hours in at the bench. Compare those old numbers to the new ones. See any difference? You should. When you break in an engine, you are doing just that, "breaking-in". During that period your connecting rod expanded and contracted and those bushings got worn. The piston also expanded and contracted along with the sleeve and case. Everything clean and lubricated again? How did the engine perform? Does it do what you want? Can you handle it? These are questions you need to ask before you modify that engine. What is the purpose the engine is used for? Everyday use, racing, all out speed, race course?

Using the Numbers

Finally huh? There are only a few formulas that you need to use right now. The first is to calculate the piston position in the sleeve (height) at a given moment in time (degree of the crankshaft). To do this we use the formula "Piston Travel vs. Crank Rotation" on the formulas where:

d = ((S/2) + L) - (S/2 cos X) - L sin[cos-1 (S/2L sin X)]  

   d = distance

   S = Stroke (in/mm)

   L = Connecting Rod Length (in/mm)

   X = Crank Angle Before or After TDC (deg)

Lets say that our connecting rod is 1.385 in. in length from center to center of the bushings and our stroke is 0.70 in. from TDC to BDC and our crankshaft has moved 90 degrees. Get out your calculator and solve the formula. Your answer should be -0.39495 in. or -10.03182 mm. You may need to use the alternate formula for some calculators. That is how far the piston moved with 90 degrees of crank rotation.

We have gone from degrees to inches, now lets do it from inches to degrees since distance is what we know. Try this formula in your calculator.

  D = acos (B^2+C^2-A^2) / (2*B*C)

  acos = cos^-1 for your calculator

  C = stroke/2

  B = C + A - (measured piston height)

  A = Connecting rod length

Now you should be able to determine the timing of your engine from the dimensions you recorded !!!!!

After calculating the position of the piston at 90 degrees, place your crank at 90 degrees and measure it. I tried this and got an entirely different measurement. Why? I don't really know and am looking into it. If you can figure it out let me know. Here is what I have:

Bore:                    0.8520

Stroke:                  0.697

Connecting rod length:   1.38

Calculated piston height:  0.393 in. @ 90 degrees

Measured piston height:    0.329 in. @ 90 degrees

Difference of:             0.064 in.

If we use the reverse formula to calculate a piston height of 0.329 in. we get 79.62599 degrees.

I have found why they were not the same. I did not use a degree wheel to set the timing mark of 90 degrees. I eyeballed it. Well I found out how easy it is to misjudge a crank angle and learned a valuable lesson, measure. Hope this teaches you too. Calculators don't lie, liars calculate. :-)

Modifying Your Engine

You now have the tools to change the timing of your engine without any guess work. Now lets get started. First we need to determine what timing we want to change and where to set it. 

The Tuned Pipe

I am not a self-proclaimed expert on tuned pipes or any of the other areas I have discussed In these pages. I am attempting to assemble information and explain, in a lay-persons terms, things that must be understood in order to achieve satisfactory performance from our 2-stroke engines.

It has been said that the single most performance gain that one can achieve is by strapping on a tuned pipe. This is very true if it is done properly. Don't just go down to your hobby shop and purchase a pipe marked ".21 Tuned Pipe" or ".45 Tuned Pipe", it's not that easy unless of course the pipe happens to be manufactured by the same company that made your engine. Which still doesn't guarantee that you will achieve optimum performance for your application. Remember that a pipe is determined by RPM not engine size.

What are the sections of a tuned pipe called? What does each section of the pipe do? What are negative and positive sound waves? What won't a pipe do? These are some of the questions I will try to answer here.

Sections of a Tuned Pipe

Header - Attaches to the engine and is the straight or slightly divergent (opens up 2-3 degrees) section of the pipe. It helps to suck the exhaust gases out of the engine. The header pipe cross-sectional area should be 10-15% greater than the exhaust port window for when maximum output at maximum RPM's is desired. In some cases the area of the header pipe may have a cross-sectional area 150% of the exhaust port area. the length should be 6-8 of its diameters for maximum horsepower, for a broader power curve 11 times pipe diameter may be used. The part you trim off to tune.

Divergent (Diffuser) Cone - The section of the pipe that attaches to the header and opens up at an angle like a megaphone. It intensifies and lengthens the returning sound waves thus broadening the power curve. The steeper the angle the more intense the negative wave returns, but also the shorter the duration. The lesser the angle, of course, returns a less intense wave, but for a longer period of time (duration). The outlet area should be 6.25 times the inlet area. 7-10 degree taper angle.

Belly - Located between the divergent and convergent cones, it's length determines the relative timing of the negative and positive waves. The shorter the belly the shorter the distance positive waves travel and the narrower the RPM range. This is good for operating at HIGH RPM only. The longer the belly the broader the RPM range. The diameter of the belly has little or no effect.

Convergent (Baffle) Cone - Located after the belly and before the stinger, reflects the positive waves back to the open exhaust port and forces the fresh fuel mixture back into the combustion chamber as the exhaust port closes. The steeper the angle the more intense the positive wave and the gentler the angle the less intense. 14-20 degree taper angle. The taper angle primarily influences the shape of the power curve past the point at which maximum power is obtained.

Stinger - Located at the opposite end of the pipe from the header and after the convergent cone, it is the "pressure relief valve" of the pipe where the exhaust gasses eventually leave the pipe. The back pressure in the pipe is caused by the size (diameter) or length of the stinger. A smaller stinger causes more back pressure and thus a denser medium for the sound waves to travel in. Sound waves love denser mediums and thus travel better. A draw back to a small stinger is heat build up in the pipe and engine. DO NOT USE TOO SMALL A STINGER! The stinger diameter should be .58-.62 times that of the header pipe and a length equal to 12 of it's own diameters.

When your engine fires it detonates the fuel mixture in the combustion chamber, pushes the piston down, opens the exhaust port and allows the burnt gases to escape along with the sound wave produced when the engine fired. The negative sound waves pull the exhaust gasses out of the exhaust port. The positive sound waves, reflected back from the convergent (baffle) cone, force the fresh fuel mixture back into the combustion chamber through the exhaust port thus super-charging your engine.

IMPORTANT!!!

When using the formulas above for designing or calculating what parameters the pipe to buy should have, the first step is to calculate D1. When you calculate D1 with the D1 formula above, remember that the number is in sq-in and must be converted to the diameter of the header pipe. Do this by dividing your calculation by Pi and then taking the square root. This will give you the radius of the header. Just multiply it by 2 to get the diameter. What you are doing is working the formula for the area of a circle backwards (Area of a circle = Pi r^2). From this point on, no other conversion should be necessary unless you use metric instead of English.

Selecting a Tuned Pipe

An ideal tuned pipe is thought to have a gently divergent header pipe to keep exhaust gases at a high velocity near the exhaust port opening, then a second medium diverging cone and a third high diverging cone attached to the belly. In reality it is what works for you. So how do you determine all these things? One at a time. Let's look at setting up an engine for course racing.

What do we want?

1) Quick acceleration

2) Broad RPM range

3) Broad to lower power range

This means we are probably not going to turn the maximum RPM's that the engine is capable of anywhere on the course. If our engine is capable of turning 25,000 RPM's, we will probably only use up to 20,000 RPM's. Look at each section of the pipe in the above descriptions. The Header cross-sectional area should be at least 10-15% greater than the area of the exhaust port. Length at this point doesn't really matter (at least 8 diameters), but make sure it is long enough to work with. The divergent cone would be at a medium angle for a broad power curve at lower RPM's. The belly would be medium to long for a broad RPM range. The convergent cone would be at a gentle angle because we want the duration of the positive wave to be longer.

How long is the pipe? If we go back to the formulas and get the formulas for Exhaust Systems Tuned Length and Length of Curved Pipe (if you need to calculate a curved pipe) we can calculate closely the pipe length. The formula for determining the length is:

L_t = (E_o x V_s) / N

Where:

L_t = tuned pipe length, in inches

E_o = exhaust open period, in degrees

V_s = wave speed in feet-per-second (1700 ft/sec at sea level)

N = crankshaft speed, in RPM

Let's say, for example, we have an engine that will turn 25,000 RPM. We calculate that we will only use 20,000 of those RPM's and our exhaust duration is 180 degrees. Then we substitute in the formula:

L_t = (180 x 1700) / 20,000

L_t = 15.3 inches

Now this is where you need to make a personal decision. Some people say that this distance is measured from the exhaut port opening and some say that the distance is from the center of the cylinder. The choice is yours, but I take the longer distance, which is from the exhaust port opening. Remember that this is not the total length of the pipe. This is the length from the (in my choice) face of the piston at the exhaust port to the center of the convergent cone including the invisible intersection of the convergent points not just what you see. Go back to the formulas and get the formula Baffle Cones to determine this point.

A fun little JAVA script Tuned Pipe Design program can be reached from my home page.

I have used broad terms here, such as gentle angle and steep angle, long and short, but what is gentle, steep, long and short. Well I don't really know myself. All I can suggest is ask others what works for them, look at the pipes others use and how their planes/boats/cars perform and examine the pipes in your local hobby shop. Get in touch with the manufacturer or distributer for your engine and ask them. I do know that some 40-45 engines will use a pipe designed for 60-65 engines VERY well.

Update Note - As a general rule the convergent cone should have twice the angle of the divergent cone and the largest taper angle you should use is 20 degrees and the smallest is 14 degrees. That means the divergent cone should be no more than 10 degrees and no smaller than 7 degrees.

Tuning That Pipe

Now comes the fun part! We get to go to the lake/flying site/road course again, unless of course we have our very own dyno. Not. So we have set the pipe up so that we have an optimum length. Well take it off! That's right, take it off. First we want to get the right prop, right fuel and right needle before we even mess with that pipe. You see this is where the "What a pipe can't do?" comes in. A pipe cannot make up for poor engine setups and crappy props. A pipe also cannot make up for bad engine timing and some engines are timed so poorly that no pipe will increase performance. Ok, we make a few runs without the pipe. We have the right prop, the right needle setting and this is the fuel we are going to be racing with. Put the pipe back on richen the needle a little (1/4 turn) and make a run. We pay close attention to what the engine is doing. If the engine turns slower, something is wrong, if the mixture is correct the pipe is too long. Shorten it by 1/8" at a time until the revs start to rise. If the pipe is too short the motor will run harshly and the needle setting will be unstable and critical. Add 1/8" to the length at a time. When the pipe is at the proper length you will experience the thrill of a lifetime. You will hear the engine and pipe become one in resonance. You will see your boat/plane/car accelerate like you walked behind it and gave it a kick in the rear. Bring it in, settle down and have a cold brewski and rejoice. You have succeeded in tuning that pipe.!!!

Carburetors

In the February '98 issue of RCMB, John Finch has a good article on picking a carburetor for your engine. I've known John since the early '70's as club members in the Old Dominion Model Boat Association. He has gone on since then to become one of the more respected authorities on R/C model boats especially in the mono classes where he specializes.

John suggests the following carburetor bores to be used for the specified engines.

Suggested Carburetor Selection Chart

This is a good start , but I think that we need to know more in order to make a better selection. For instance, how long or deep should the barrel be, what is the correct depth for the needle valve body assembly?

For the answers to these questions I turned to Gordon Jennings book "2-Stroke Tuners Handbook" referenced in my Formula page. The general rule for sizing the carburetor bore and length is that the length of the barrel from the opening to the center of the needle valve should be 1.5 to 1.6 times the bore diameter. The bore can be calculated with "Carburetor Throttle Bore Diameter" formula .

D = K x SQRT( C x N )

    D is throttle bore diameter, in millimeters

    K is a constant ( approx. 0.65 to 0.9, derive from existing carburetor bore)

    C is cylinder displacement, in liters

    N is RPM at peak power

    i.e.; 80 cc = .08 liters

             1 ci  = 16.39 cc

For this example let's say that we have 7.5 cc (.45 ci.) engine which produces it's maximum power at 20,000 rpm. Therefore:

C = .0075 liters

N = 20,000

K = .65

D = 0.65 x SQRT(.0075 x 20000)

   = 0.65 x SQRT(150)

   = 0.65 x 12.247

   = 7.96 mm

   = 0.3134 in.

If we use K = 0.9 then D = 0.433

Pretty darn close to John's suggested sizes huh? But now you know how and why, not just at random, he chose those numbers. Using the ratio I quoted above, the depth of the bore to the center of the needle valve will be approximately 0.470 in. for a bore of 0.3134 and 0.65 in. for a bore of 0.433.

Guess your wondering how far from the center of the needle valve to the bottom of the carb we should be? Me too! The only reference to this I could find is that maximum air flow will be obtained with the carb located close to the intake port window, but it also gives the poorest mixture delivery. Locating it further away from the port reduces volumetric efficiency, but provides the best mixture-strength stability.

At this point I should point out a phenomena that occurs inside the carburetor. The air drawn into the carburetor actually passes the needle three times. Air passes the nozzle moving into the intake tract, then reverses direction as the result of the pulse generated when the intake port chops shut, and passes the spray nozzle a third time as the next intake period begins. You can actually see this if you look carefully at the intake of your carburetor when the engine is running at medium rpm. You will see fuel trying to exit the carburetor.

The end of the spray bar should be located exactly in the center of the carburetor barrel.

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