How big is first order part of reaction torque?

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Niels Abildgaard

Well-Known Member
Jun 13, 2010
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I want a new toy.
Swan 120 SW

Expensive toy

I am not keen on engine that is a hard pressed single cylinder Pollini 303 (38 hp/8000rpm) with a reduction gearing turning a 1.5m prop ca 42 rps.
Can of course make something better but will have to make a model to show all the doubting,wise guys with money.
Scheme is an inverted,four exhaust valved two stroke with first order mass balance shaft.
Prop act as flywheel and reliability is good.

This balance shaft turns opposite direction to crank and make engine as harsh or pleasant as a normal four cylinder four stroke with same total piston and conrod mass.
The underhung camshaft rotates same way as crank and can eliminate the first order part of the torque variation for one load condition (So called 70% power whatever definition is most valid.)

UHC wonder engine.
Ideally, a balance shaft would be concentric with the crankshaft, so that it does not generate a secondary vibration due to the offset between centres of rotation.

If we consider the counterweights on a normal crankshaft viewer from the end, they move both up and down (opposing the mass of the piston and rod) and side to side.

If the counterweights were of the same mass as the piston and rod, they would completely balance them on the up and down direction, but they would create vibration in the side to side direction. That vibration would be equal to the vibration of the same engine with no counterweights, just shifted from up and down to side to side.

This issue is normally dealt with by using a balance factor. This means the counterweights are, say, 70% of the mass of the piston and rod, so they balance out most of the up and down vibration, and generate a smaller side to side vibration.

If the counterweights on the crankshaft are only 50% of the piston and rod mass and we have another equal pair of counterweights turning on the opposite direction around the crankshaft axis, between them they can balance out all of the piston and rod vibrations in the up and down direction, but the counterweights also balance each other in the side to side direction.

Of course, it is not quite so simple, because the lower end of the rod is actually moving in a circle, not up and down. The rods is also swinging from side to side, so you'll will always have some degree of vibration, but the counter rotating balance weights can reduce overall vibration to a very low level.

It should be noted that the gears required to drive the second set of balance weights will need to need quite substantial, as they will need to transmit the shock load of each firing stroke to the weights.
It is unforgiveable not to minimize mass of piston and conrod for single cylinder engines.

CAD system calculates mass and center of gravity very precisely.

Crank is develloped to minimum mass on the buisness side and then put all the contra mass on as possible.

Ballance shaft as basicly a semidisc not colliding with rest of machinery.

Bring the parts in these two situations and let computer calculate coordinates for center of gravity for both situations.
bai first nw.JPG
bai first se.JPG

In these situations (45degree)second order forces are zero and the arrangement cannot do anything against them anyway.
Trick is now to remove as much unnessecary mass(CAD) from counterweigths and balance shaft and get center of gravity for each assembly to be so close as possible.
Takes a little time.
We now have best first order mass balance and no first order forces coming out
Exactly like a normal fourcylinder regular firing fourstroke with same piston and conrod mass.

First order means one sine-wave per revolution
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The crankshaft counterweights can balance much of the first order vertical (up and down) imbalance, but not the first order side to side created by the counterweights and conn rod. A single balance shaft rotating at the same speed as the crank can eliminate much of first order side to side imbalance (rocking) but not the 2nd order imbalance at 45, 135, 225, and 315 degrees. Using 2 counter-rotating balance shafts at twice the crank speed can eliminate much of the the rocking first order (90 and 270) and also much of the 2nd order at 45,135,225, and 315. A point of diminishing returns is reached with each iteration because of the inherent unsolvable problem of the conn rod moving both in a circle and up and down. You can get a little closer each time but at the cost of continually increasing complexity.

All balancing is a compromise. And the question of, "when is good enough, good enough?"

My 2 cents. Lloyd
I spend time dreaming up best possible single person aircraft 30kW/40 hp engine,
Be for ultraligth,paraplane or experimental.
Slim people can fly in normal looking aircrafts on ca 30 horsepower if wings are long and/or structure very ligth.
40 horsepower is better and hangar hire less.
One concept is an inverted ,single two stroke cylinder with 100mm bore and 150mm stroke.

The Balancing procedure can maybee interest others,so I will try to describe it step for step
bevæg.postal jpg.jpg
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I have designed piston,rings,pin,conrod and buisness parts of crank to the best of my knowledge for lowest possible mass.
First step is to remove so much material from crank countermass that comon center of gravity always stays on cylinder centerline.
The mass of mowing parts is 5,86kg that is mowing from 17.8mm to 40,6mm below crank centerline and back during one revolution
balance move postal top.jpg
balance move postal midt.jpg
balance move postal tbund.jpg

.Done 40 times a second is quite some shaking
One could expect that the 90 degree situation will have common center mowing parts midway between
17,8 and 40.6 that is 29,2mm but it is at 26,8 and this is due to the shortness of conrod and this gives trouble as second order shaking forces that are much more cumbersome to remove.
Their disturbance are not insignificant and modern fast reving four-cylinder ,inline, fourstroke engines can have two balanceshafts that turn twice as fast as crank to ease vibration problems and uncomfort..
For an aircraft engine it is maybe to much mass and faultsource.
I will not propose a single-cylinder two stroke aircraft engine with second order balancing.

Let us put a crank-counter-rotating balanceshaft on the crank centerline and dimension it so that this first order up and down shaking forces from piston movement can be eliminated.

In that case it is enough to observe movement of common center of gravity for moving parts as in letter 4 that is 45 degree before top and bottom where sencond order forces are zero.
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Some engines had 2 balance shafts to neutralize the off center vibration induced by 1 balance shaft. And then you have to look at any of the harmonics that exist in the mass of the engine block. You are trying to balance the crank, rod, piston and block mass, and any harmonics that exist in that assembly, and are then adding more moving mass which will in turn shift the harmonics of the whole system.
If your engine is 2 stroke, how is scavenge pressure provided?
Using crankcase as scavenge pump the good old way.
A scavenge expert said that due to undersquareness and uniflow,, brake mean pressure can be 8.5 bar or ca 68 horsepower at 3000 rpm.
I need 40 horsepower at 40 rps and therefore ask for a BMEP of ca 6.25.
A present family car with variable intake length achieve ca 12 bar.
No supercharger.
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@Niels Abildgaard

Niels, might I suggest you take a look at this.
I just purchased his crank balance calculator spreadsheet for my 2 stroke diesel and it is very very extensive and complete. The what-ifs for the design phase are pretty much limitless once you get the hang of using the spreadsheet. You modify the shape of the crank by inserting equivalent holes or weights that have the same weight and CG as in the actual crank. There are entries for the oddities of your conn rod, a balancer. It is not a super slick $400 program, but it is a nice spreadsheet and the formulas he uses are not hidden, so you can actually see what he is doing. For only $30USD it seems like a real bargain. But it will still be a few months till I get the model spinning to know how it really works.

It will require an investment in your time to get the most out of it.
Using crankcase as scavenge pump the good old way.
A scavenge expert said that due to undersquareness and uniflow,, brake mean pressure can be 8.5 bar or ca 68 horsepower at 3000 rpm.
I need 40 horsepower at 40 rps and therefore ask for a BMEP of ca 6.25.
A present family car with variable intake length achieve ca 12 bar.
No supercharger.
In that case don't forget about filling up the crankcase volume so your crankcase compression ratio is high enough. You might have to use flywheel type crank just to take up the volume.
Having looked at the programe from dragonfly I prefer (surprice,surprice) to do it my way.
Efficiency of crankcase pumping for two strokes is debatable matter.
.If we ad some countermass to crank we can have less up and down but get some sideways and have ,of course, more mass.
balance move.jpg

Sideway movement of COGMP is now ca 10.3mm and up and down is ca 10.28mm
Total mass of mowing parts are now 6.5 kg.
To achive the non plus ultra we introduce a counterrotating balance shaft.
For calculating and understanding we put centerline of balanceshaft coincident with crank centerline
We have now 7.4 kg and COGMP do not move sideways and is mowing up and down ca 2 mm two times each revolution.
This shows why project never went places.
With two opposed cylinders there is no free forces going out bee they first or second order and the corresponding mass will be 3.3kg.

Nobody puts 4 kg extra in a 40 horsepower aircraft engine.
balance move  fuld vandret.jpg
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Have been reading around and will like to change dimension of goal.
There is company working on postal UAVs and they use two 27horsepower/60 rps industrial V twins for propulsion.

Flying Postman

Same engine/ power (Serie 38 from B&S) are used by quite some homebuilt aircrafts named MC30 Luciole.

12 meter per second mean piston speed is a good aircraft number and 60 rps is fit for noise regulations for our direct drive propellers (1200mm dia) so we start with 100mm stroke.

A real two stroke expert told me that a crankcase scavenge system like the one shown in letter 6 can easily pump for a Brake Mean Effective Pressure of 8.5 bar.

Around 400 ccm and in relation to our 100mm stroke this is ca 72mm bore.

27 horsepower is very close to 20kW and at 60 rps this gives a mean torque 53 Nm.

A very rough mass estimate for my RoXaX 400ccm engine can be had from mass per litre for pre-WW2 inline four stroke aircraft engines and they were all around 28 kg/litre and ran at same effective mean pressure.
RoXaX 20 should be able to mass out at 12 kg Plus all that balancing stuff.
The B&S engine mentioned is not less than 24 kg so we can still seek public or silly money.
For the Windracer drone it means that usefull load can be 125 kg instead of 100 kg.
We still have uncompensated second order mass forces and a rather unpleasant varying countertorque.
FIAT makes and installs a two cylinder fourstroke in some cars and they works but are not smooth or classy.
Same vibration level and harshness as a single cylinder two stroke with first order mass balance for same power.

Time to move on and allmost all drone and UAV engines sold to day are boxer- two- strokes two or four cylinders.
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20kW at 60 rps at a mean piston speed of 12 m per second can be schemed as a two cylinder two-stroke exhaust valved engine with cylinder bores of 66mm and strokes of 100mm.
USA made more than 76000 mcculloch o-100 four cylinder two strokes that ran with a BMEP of 6 bar and mass per litre ca 21 kg.
My NoTax engine is .7 litre and need a BMEP of 5 bar to make 20kW at 60 rps.
Again ca 12 kg plus the balance gear that makes it behave torque-wise as a four cylinder boxer (two- or fourstroke).

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Now comes where expert help is needed.
The mean torque is what turns the propeller and is arond 53Nm
The reaction torque will vary from ca minus 50 to ca plus 250 Nm.
This can be split in mean (zero order but useful for us) ,first order sine wave second order etc that make us miserable and fatiques structure of plane.
I have forgoten how to analyse for harmonics but seem to remember that for a two stroke cylinder, doing usefull work,, the first order amplitude is ca two times mean value or in our case ca 100Nm
If we dimension the two co-rotaing cam/balace shafts so that they give a torque of ca 50 Nm thirty crank degree after top and bottom dead centers we are in fourcylinder land with only two cylinders.
There are no second order free forces in the boxer.
The inverted single cylinder (or an inline twin) as shown in letter 6 has a lot .
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The distance between cam-/balance shafts can be around 280mm in my latest version.
One revolving unbalance shall therefore give a centrifugal force of 50/0.28 or ca 180 Newton when doing 60 rps.
If my calculationd are correct that is a point mass of 42 gram or 6ccm steel circling 30mm from shaft axis.Even using tungsten will not be a deal breaker
I will use rest of day checking as it sounds unrealistic little.
On the other hand it seems that the camshaft drive belt or chain wheels are the natural place for said unbalances.
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