cylinder ratios
cylinder ratios
Hi,
Been doing some research regarding the ratio between the displacer cylinger and the power cylinder.
I've been unable to find the ratio between the diameters. I know the swept volume is to be 1.33 percent. but what diameter difference would there be?
The obvious difference would be a change in how far the displacer would have to travel for a equilalent "swept volume". What impact in performance would that have?
Wayne
Been doing some research regarding the ratio between the displacer cylinger and the power cylinder.
I've been unable to find the ratio between the diameters. I know the swept volume is to be 1.33 percent. but what diameter difference would there be?
The obvious difference would be a change in how far the displacer would have to travel for a equilalent "swept volume". What impact in performance would that have?
Wayne

 Posts: 66
 Joined: Tue May 16, 2006 5:06 pm
 Location: California
Hi Wayne,
Welcome to the forum! A couple of simple formulae to keep in mind.
1) The displacer cylinder is ideally divided into 1/3 cool and 2/3 hot. The displacer itself should be about 2/3 the total length of this cylinder. Also the ratio between the displacement volumes of the two cylinders is 33% larger for the displacer cylinder or 1.5 times the power cylinder.
2) Remember the formula for the volume of a cylinder? V=(height)(radius)²π
so:
1.5(volume of power cylinder)=(volume of displacer cylinder)
1.5(heightP)(radiusP)²π=(heightD)(radiusD)²π
1.5(heightP)(radiusP)²=(heightD)(radiusD)² (pi cancels out)
and if we make the height of the power cylinder the same as its diameter (which is suggested for a compromise between power and speed)
1.5(2)(radiusP)(radiusP)²=(heightD)(radiusD)²
3(radiusP)³=(heightD)(radiusD)²
Now your best bet is to select your radii based on the materials you can obtain, then determine the height of your displacer.
I'm not sure if I've ever seen anything written about the travel distance of the displacer or if it really is significant in affecting the engine's performance. What I can say is that the travel distance of the power piston (the "stroke") does have an affect. Given an equal displacement volume for two engines, one with a shorter throw applies its force to a shorter crank than an engine with a longer stroke. This shorter throw in turn is more useful in higher speed engines while the longer throw is more useful for high torque applications.
Hope that answers you questions, but if not be sure to write back and I'll try again.
Stefan
Welcome to the forum! A couple of simple formulae to keep in mind.
1) The displacer cylinder is ideally divided into 1/3 cool and 2/3 hot. The displacer itself should be about 2/3 the total length of this cylinder. Also the ratio between the displacement volumes of the two cylinders is 33% larger for the displacer cylinder or 1.5 times the power cylinder.
2) Remember the formula for the volume of a cylinder? V=(height)(radius)²π
so:
1.5(volume of power cylinder)=(volume of displacer cylinder)
1.5(heightP)(radiusP)²π=(heightD)(radiusD)²π
1.5(heightP)(radiusP)²=(heightD)(radiusD)² (pi cancels out)
and if we make the height of the power cylinder the same as its diameter (which is suggested for a compromise between power and speed)
1.5(2)(radiusP)(radiusP)²=(heightD)(radiusD)²
3(radiusP)³=(heightD)(radiusD)²
Now your best bet is to select your radii based on the materials you can obtain, then determine the height of your displacer.
I'm not sure if I've ever seen anything written about the travel distance of the displacer or if it really is significant in affecting the engine's performance. What I can say is that the travel distance of the power piston (the "stroke") does have an affect. Given an equal displacement volume for two engines, one with a shorter throw applies its force to a shorter crank than an engine with a longer stroke. This shorter throw in turn is more useful in higher speed engines while the longer throw is more useful for high torque applications.
Hope that answers you questions, but if not be sure to write back and I'll try again.
Stefan

 Posts: 1
 Joined: Mon Dec 11, 2006 12:37 pm
Dear Stefan,
In regards to your reply to Wayne on displacer/P.piston ratios, I have a couple of questions if you or others could address:
First, where does the displaced volume number of 33% come from?
I would be interested in the derivation or reference there to. Is the volume ratio dependant upon the 'working fluid'? i.e, (air vs H vs He vs C3H8 vs other?)
Second; you mention compromise between power & speed....
Would not power be dictated by volume of power piston? (and therefore related to displaced volume and therefore related to surface areas in hot & cold reservoirs, etc?)
Once a volume is set, is the trade space more clearly thought of as
between speed (rpm) and Torque?
My thinking has the power fixed to P.piston volume but you could build for hightorque, low speed, or lowtorqu, highrpm.
Please correct or redirect me if this is in error.
Next: ( This is fun stuff I've lots of questions )
Heat transfer to working fluid seems critical, as does heat extraction. Would these sections of the displacer cylendar be better isolated? I'm thinking it would be interesting to use a section of pirex, say the straight sided globe of a small lantern, as a viewport/thermal isolator between Qh & Qc sections.
=OR=
does the ~warm, inbetweenland, of metal cylendar wall act as regenerator/heat balast for the air?
Has anyone played with the idea of using a semiporous or channeled displacer so that the displacer itself could act in part as a regenerator with the gasses traveling through it?
In lay terms: Is the regenerator acting as an energybalast allowing for a smaller engine by reducing the requisite fluidmassvolume? That is, if you have the space, could you forgo the regenerator in lieu of a larger working volume?
Thank you for your help with these ideas:
I am facinated by the walking beam engines and so will probably undertake such over the holidays.
Derivations for/against these arguments are most welcome.
Thanks,
Gary
[/quote]
In regards to your reply to Wayne on displacer/P.piston ratios, I have a couple of questions if you or others could address:
First, where does the displaced volume number of 33% come from?
I would be interested in the derivation or reference there to. Is the volume ratio dependant upon the 'working fluid'? i.e, (air vs H vs He vs C3H8 vs other?)
Second; you mention compromise between power & speed....
Would not power be dictated by volume of power piston? (and therefore related to displaced volume and therefore related to surface areas in hot & cold reservoirs, etc?)
Once a volume is set, is the trade space more clearly thought of as
between speed (rpm) and Torque?
My thinking has the power fixed to P.piston volume but you could build for hightorque, low speed, or lowtorqu, highrpm.
Please correct or redirect me if this is in error.
Next: ( This is fun stuff I've lots of questions )
Heat transfer to working fluid seems critical, as does heat extraction. Would these sections of the displacer cylendar be better isolated? I'm thinking it would be interesting to use a section of pirex, say the straight sided globe of a small lantern, as a viewport/thermal isolator between Qh & Qc sections.
=OR=
does the ~warm, inbetweenland, of metal cylendar wall act as regenerator/heat balast for the air?
Has anyone played with the idea of using a semiporous or channeled displacer so that the displacer itself could act in part as a regenerator with the gasses traveling through it?
In lay terms: Is the regenerator acting as an energybalast allowing for a smaller engine by reducing the requisite fluidmassvolume? That is, if you have the space, could you forgo the regenerator in lieu of a larger working volume?
Thank you for your help with these ideas:
I am facinated by the walking beam engines and so will probably undertake such over the holidays.
Derivations for/against these arguments are most welcome.
Thanks,
Gary
[/quote]

 Posts: 66
 Joined: Tue May 16, 2006 5:06 pm
 Location: California
Hi Gary,
The proportions I used in my equations came from Roy Darlington's book: Stirling and Hot Air Engines and James Rizzo's Stirling Engine Manual. Their explanation is that the onethird twothird ratio was derived experimentally by Stirling. I believe that it assumes air as the medium.
I stand corrected in terms of the description of power output. Naturally, the power doesn't change, rather the speed and torque. Good catch!
Your questions about the displacer and heat transfer are terrific. One common modification of the displacer is to create it out of tightly packed steel disks or steel wool wound tightly around its shaft. This "porous" displacer does, in fact, act as regenerator. Even a standard displacer has some regenerating effect by creating a gradient of heat along its length.
As for the separation between the two sides of the displacer cylinder, I've considered doing this myself, though the practicality of its manufacture has been my sticking point. It has to be airtight, create no additional dead space, allow free movement of the displacer, and actually provide a thermal barrier.
Let us know how your project turns out!
Stefan
The proportions I used in my equations came from Roy Darlington's book: Stirling and Hot Air Engines and James Rizzo's Stirling Engine Manual. Their explanation is that the onethird twothird ratio was derived experimentally by Stirling. I believe that it assumes air as the medium.
I stand corrected in terms of the description of power output. Naturally, the power doesn't change, rather the speed and torque. Good catch!
Your questions about the displacer and heat transfer are terrific. One common modification of the displacer is to create it out of tightly packed steel disks or steel wool wound tightly around its shaft. This "porous" displacer does, in fact, act as regenerator. Even a standard displacer has some regenerating effect by creating a gradient of heat along its length.
As for the separation between the two sides of the displacer cylinder, I've considered doing this myself, though the practicality of its manufacture has been my sticking point. It has to be airtight, create no additional dead space, allow free movement of the displacer, and actually provide a thermal barrier.
Let us know how your project turns out!
Stefan
Hi Stefan,
I was reading your post of Dec 12. You mentioned using steel wool for the displacer, tightly wound on the shaft. I was wondering if you had tried it and how did it work with the tin can engine? I have found one other mention of this on the 'net' and it caught my attention, especially if it is lower weight! I picked up a few boxes of stainless steel scrubber (Chore Boy brand) but not sure if it will pack tightly enough. I was thinking of using this on my second engine but I don't want to be wasting my time if someone has already tried it and it didn't work.
Thanks for any information,
Donnie
I was reading your post of Dec 12. You mentioned using steel wool for the displacer, tightly wound on the shaft. I was wondering if you had tried it and how did it work with the tin can engine? I have found one other mention of this on the 'net' and it caught my attention, especially if it is lower weight! I picked up a few boxes of stainless steel scrubber (Chore Boy brand) but not sure if it will pack tightly enough. I was thinking of using this on my second engine but I don't want to be wasting my time if someone has already tried it and it didn't work.
Thanks for any information,
Donnie

 Posts: 66
 Joined: Tue May 16, 2006 5:06 pm
 Location: California
Hi Donnie,
I haven't tried it myself, though like you I have found several sources that mention it. Perhaps you could design your engine with a replaceable displacer so that you could try different configurations? It's a bit more work to make the cylinder openable, but I have found it a great deal easier to experiment and perform maintenance on my engines.
Stefan
I haven't tried it myself, though like you I have found several sources that mention it. Perhaps you could design your engine with a replaceable displacer so that you could try different configurations? It's a bit more work to make the cylinder openable, but I have found it a great deal easier to experiment and perform maintenance on my engines.
Stefan

 Posts: 35
 Joined: Sun Apr 29, 2007 9:24 am
it is generally said that 1,5 volume ratio between power and displacer cylinders is desirable. Where does this number come from?
I know engines with ratio less than 1,5 will have difficulties to run properly, but what would happen if the ratio was greater than 1,5? If the displacer cylinder free volume is more than 1,5 times the power cylinder swept volume, what would this do to the engine's performance? I quess some work done would be lost moving a larger displacer, but any other pros or cons?
I know engines with ratio less than 1,5 will have difficulties to run properly, but what would happen if the ratio was greater than 1,5? If the displacer cylinder free volume is more than 1,5 times the power cylinder swept volume, what would this do to the engine's performance? I quess some work done would be lost moving a larger displacer, but any other pros or cons?
Alpha,
The ratio 1.5 to 1 I believe is for the best efficientcy for power produced by a typical Stirling cycle engine. This seems to be a base line to work with. LTD Stirling's use a much larger displacer to power cylinder volume. Mine have been about 10 to 1 and run well on very little heat. Your right about the power required to move a larger displacer with a small power cylinder and if your going to make a LTD that runs well (or at all) your friction must be extremely low and your displacer very light. You can use ratio's other than 1.5 to 1 and more or less heat respectively. Also, an engine with a large displacer running on lower heat will likely run at low RPM too. If you want a faster spinning engine stay closer to the 1.5 to 1 (stroke will also have a large effect on RPM but you already know that.) A good rule of thumb I've not seen mentioned much is to have bore diameter equal to stroke, that is known as a "square" engine. An engine with too long of a stroke will have too much friction since the side loads on the piston will be increased. Long connecting rods help reduce side loads but staying closer to "square" is generally better in my opinion.
The ratio 1.5 to 1 I believe is for the best efficientcy for power produced by a typical Stirling cycle engine. This seems to be a base line to work with. LTD Stirling's use a much larger displacer to power cylinder volume. Mine have been about 10 to 1 and run well on very little heat. Your right about the power required to move a larger displacer with a small power cylinder and if your going to make a LTD that runs well (or at all) your friction must be extremely low and your displacer very light. You can use ratio's other than 1.5 to 1 and more or less heat respectively. Also, an engine with a large displacer running on lower heat will likely run at low RPM too. If you want a faster spinning engine stay closer to the 1.5 to 1 (stroke will also have a large effect on RPM but you already know that.) A good rule of thumb I've not seen mentioned much is to have bore diameter equal to stroke, that is known as a "square" engine. An engine with too long of a stroke will have too much friction since the side loads on the piston will be increased. Long connecting rods help reduce side loads but staying closer to "square" is generally better in my opinion.

 Posts: 35
 Joined: Sun Apr 29, 2007 9:24 am
so... I'm converting my failed alpha engine (I needed to heat it red hot with acetylene flame to get it even turning) into gamma engine. My power cylinder bore is 25mm (1") and the stroke is about 30mm (1.2"). The stroke of the displacer would be the same 30mm. I calculated that If I gave the displacer cylinder total length of 105mm (4.1"), the bore should be 30mm (1.2"). The length of the displacer piston should be 70mm (two thirds of the total length of the cylinder, leaving it plenty of room to move).
Free volume in the displacer cylinder would be 35mm * 15^2 *(pi) =24740mm^3
The maximum volume of power cylinder is 35mm * 12.5^2 (pi) = 17180mm^3
the ratio between these volumes is 1.44, which can be heightened by making the power piston stroke shorter. Am I correct with these assumptions? If not, from which volumes does the ratio come from?
Free volume in the displacer cylinder would be 35mm * 15^2 *(pi) =24740mm^3
The maximum volume of power cylinder is 35mm * 12.5^2 (pi) = 17180mm^3
the ratio between these volumes is 1.44, which can be heightened by making the power piston stroke shorter. Am I correct with these assumptions? If not, from which volumes does the ratio come from?
SScandizzo wrote:Hi Wayne,
Welcome to the forum! A couple of simple formulae to keep in mind.
1) The displacer cylinder is ideally divided into 1/3 cool and 2/3 hot. The displacer itself should be about 2/3 the total length of this cylinder. Also the ratio between the displacement volumes of the two cylinders is 33% larger for the displacer cylinder or 1.5 times the power cylinder.
2) Remember the formula for the volume of a cylinder? V=(height)(radius)²π
so:
1.5(volume of power cylinder)=(volume of displacer cylinder)
1.5(heightP)(radiusP)²π=(heightD)(radiusD)²π
1.5(heightP)(radiusP)²=(heightD)(radiusD)² (pi cancels out)
and if we make the height of the power cylinder the same as its diameter (which is suggested for a compromise between power and speed)
1.5(2)(radiusP)(radiusP)²=(heightD)(radiusD)²
3(radiusP)³=(heightD)(radiusD)²
Now your best bet is to select your radii based on the materials you can obtain, then determine the height of your displacer.
I'm not sure if I've ever seen anything written about the travel distance of the displacer or if it really is significant in affecting the engine's performance. What I can say is that the travel distance of the power piston (the "stroke") does have an affect. Given an equal displacement volume for two engines, one with a shorter throw applies its force to a shorter crank than an engine with a longer stroke. This shorter throw in turn is more useful in higher speed engines while the longer throw is more useful for high torque applications.
Hope that answers you questions, but if not be sure to write back and I'll try again.
Stefan
This is some very interesting information. I wish I had this information 20 years ago when I first started building stirling hot air engines.
GW
SScandizzo wrote:Hi Wayne,
Welcome to the forum! A couple of simple formulae to keep in mind.
1) The displacer cylinder is ideally divided into 1/3 cool and 2/3 hot. The displacer itself should be about 2/3 the total length of this cylinder. Also the ratio between the displacement volumes of the two cylinders is 33% larger for the displacer cylinder or 1.5 times the power cylinder.
2) Remember the formula for the volume of a cylinder? V=(height)(radius)²π
so:
1.5(volume of power cylinder)=(volume of displacer cylinder)
1.5(heightP)(radiusP)²π=(heightD)(radiusD)²π
1.5(heightP)(radiusP)²=(heightD)(radiusD)² (pi cancels out)
and if we make the height of the power cylinder the same as its diameter (which is suggested for a compromise between power and speed)
1.5(2)(radiusP)(radiusP)²=(heightD)(radiusD)²
3(radiusP)³=(heightD)(radiusD)²
Now your best bet is to select your radii based on the materials you can obtain, then determine the height of your displacer.
I'm not sure if I've ever seen anything written about the travel distance of the displacer or if it really is significant in affecting the engine's performance. What I can say is that the travel distance of the power piston (the "stroke") does have an affect. Given an equal displacement volume for two engines, one with a shorter throw applies its force to a shorter crank than an engine with a longer stroke. This shorter throw in turn is more useful in higher speed engines while the longer throw is more useful for high torque applications.
Hope that answers you questions, but if not be sure to write back and I'll try again.
Stefan
How does the above formula apply to a beta engine, since the volume of working fluid in the power cylinder is also affected by the movement of the dispalcer? Would it be oversimplyfing to simply base the volumetric calculations on piston diameter and stroke?
Re: cylinder ratios
At what distance should we drill the hole for power cylinder into the displacer cylinder from its top??.
How can we keep the hot area 1/3 and cooled area 2/3 of cylinder length ,if we choose displacer piston equal to 2/3
of cylinder and stroke of displacer piston equal to diameter of displacer cylinder.??
let suppose we have 6" displacer cylinder of dia 2".
Now where should i drill the whole of 1" of power cylinder into displacer cylinder.??
Also how much down should displacer piston come to the bottom of displacer cylinder. should it come down near to base
of displacer cylinder.??
How can we keep the hot area 1/3 and cooled area 2/3 of cylinder length ,if we choose displacer piston equal to 2/3
of cylinder and stroke of displacer piston equal to diameter of displacer cylinder.??
let suppose we have 6" displacer cylinder of dia 2".
Now where should i drill the whole of 1" of power cylinder into displacer cylinder.??
Also how much down should displacer piston come to the bottom of displacer cylinder. should it come down near to base
of displacer cylinder.??
Re: cylinder ratios
wlowry wrote:Hi,
Been doing some research regarding the ratio between the displacer cylinger and the power cylinder.
I've been unable to find the ratio between the diameters. I know the swept volume is to be 1.33 percent. but what diameter difference would there be?
The obvious difference would be a change in how far the displacer would have to travel for a equilalent "swept volume". What impact in performance would that have?
Wayne
The sweep area for a displacer piston is about 2/3rd of its total cylinder volume. This is Stirling practice however your number of 1.33% should be restated as 133%, the displacers cylinder lenth being a 3rd longer than the displacer piston plus a half inch more for a 1/4 inch clearance at each end of cylinder in a table top model size. You will not find these ratios until you decide what the bore and stroke will be! You want a match VOLUME for both displacer and power cyl. for a "square" built engine. Your volumes can be changed if you do change the cylinder diameters or the piston stroke. If you change ONE cyl. diameter and not the other cylinders dia, you change this ratio. If you increase/ decrease the stroke on just one cyl. , you also changed the ratio. If you are building a model Stirling you control the piston diameters and the stroke travel. The math will give you the ratio result of your design parrameters regarding stroke and diameter of the engines cylinders. If your question is about the diameter difference between the inner diameter of a displacer cyl. to the outter diameter of its displacer think in terms of clearances instead of ratios here. The displacer must move freely without contacting the cylinder. In a test tube engine the displacer should be around .080 smaller than inner cyl diameter to prevent any rubbing issues. Longboy.
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