Formulas for calculating the bore and stroke of a diesel engine

[ruben]

Hello, I would like to know if there is a formula to calculate what diameter and stroke a diesel engine should have with a compression ratio of 20 to 1 or with a compression value of 25 bars.

 

[GreenTwin]

For an engine with a 1" diameter bore, the area of the top of the piston is pie-r-squared, so 0.785 sq.in.

Assuming a clearance of 1/16", then the volume at TDC would be 0.04906 cu.in.

For a 20:1 ratio, then the volume at BDC would be 0.98125 cu.in.

So 1.25" stroke.

My math is off somewhere.
Somebody help me.

.

 

[minh-thanh]

Compression ratio depends on 2 factors: r (radius) and h (length)
There are 2 types of h: h1 is the piston stroke and h2 is the combustion chamber
If you choose compression ratio 20:1
From there you calculate the ratio of h1 and h2
If you choose h1 stroke then you can calculate h2 and vice versa
Note - the combustion chamber is not cylindrical so to calculate its volume you have to measure everywhere or you can measure it by filling the combustion chamber with liquid and measuring the volume of liquid in the combustion chamber

 

[peterl95124]

My "Hansen" Diesel has a stroke of 40mm, and a head space at TDC of 2mm, so ~20:1, diameter doesn't factor in, its that simple !!! (technically its 42:2, but 40:2 is close enough for gov't work !)

 

[petertha]

My math is off somewhere.
Somebody help me.

Using your example which assumes the combustion chamber is perfectly cylindrical, the CR calculates to 21. Bore & Pi drop out of the equation so you can get the same CR value just knowing stroke (s) & clearance (h) using CR=(s+h)/h. But typically combustion chamber is domed or angled or otherwise 'non-cylindrical' so you have to compute or otherwise measure its actual volume Vc & use formula CR=(Vd+Vc)/Vc

https://en.wikipedia.org/wiki/Compression_ratio

 

[petertha]

(for the simplified cylindrical combustion chamber example only!) if you know CR and stroke (s), h can be determined using h =s/(CR-1).

But for a 'non-cylindrical' head it becomes a convergence type solution. Example Vc was measured directly at 0.080 in3. Stroke was iterated until the target CR of 15.0 was achieved using the same CR formula. Similarly you could define the stroke & vary the bore to converge.

 

[GreenTwin]

This is one of Find Hansen's videos.
He lists a bore of 20mm, and a stroke of 40 mm, with a compression ratio of 21:1.

Obviously the clearance volume is going to have a big affect on compression ratio, and I seem to recall seeing that diesels had a relatively small clearance space.

I will see if I can match his numbers somehow.



.

 

[GreenTwin]

My "Hansen" Diesel has a stroke of 40mm, and a head space at TDC of 2mm, so ~20:1, diameter doesn't factor in, its that simple !!! (technically its 42:2, but 40:2 is close enough for gov't work !)

Seems like you are mixing your units.
You are making a ratio between length in mm and volume in cubic mm.
I think it would need to be a comparison between two cubic volumes in order to calculate the ratio of minimum to maximum pressure, which I think is the definition of compression ratio ?

Edit:
Or I guess you are saying a head clearance of 2mm, not a volume, so never mind; I am a bit confused, as usual.
.

 

[GreenTwin]

Looking at the two extremes, in one ideal case, where there is no clearance, the pressure will approach infinity as the piston approaches TDC.
In the other extreme, as the cylinder becomes infinitely long, the pressure approaches zero; ie: no compression is taking place.

I seem to recall that diesels use a relatively long stroke, with associated slower maximum rpm that a square engine, ie: a square engine having a bore that equaled the stroke.

Looking at a Detroit Diesel 671 engine, the displacement per cylinder is 70.93 cu in, with a 4.25" bore, and a 5" stroke, 18.7 : 1 compression ratio.
This is not nearly as long a stroke as I had thought was used.

So with a diesel, the key is the air inside the cylinder being compressed to the point where it reached the ignition temperature of diesel fuel; recalling the old thermo class days, and the PV=mrt forumla (I think is the correct forumula, or ballpark thereof).

So perhaps we can use the 671 data and work backwards to see what the clearance would have had to have been at TDC to get 18.7 : 1, and reach the ignition temperature required.

Obviously as the clearance goes down, the pressure and compression ratio go up.

So if Peter's forumula is correct, then a Detroit 671 would have a head clearance of 0.267", which seems reasonable.

.

 

[GreenTwin]

Working it as a volume comparision, the total volume at BDC with a 0.267" head clearance would be 74.68 cu in.

At TDC, the volume with a 0.267" head clearance (assuming a flat head and a flat piston top, to simplify things) would be 3.7857 cu in.

The ratio would be 74:68/3.7857 = 19.7 : 1

So pretty close to 18.7 : 1, but slightly off.

.

 

[GreenTwin]

I would not have thought that it would be as simple as a ratio of stroke to head space, but it does seem that way, reading what everyone has posted above.

.

 

[GreenTwin]

Hello, I would like to know if there is a formula to calculate what diameter and stroke a diesel engine should have with a compression ratio of 20 to 1 or with a compression value of 25 bars.

I am not sure about the 25 bar, but the answer seems to be to compare the stroke to the head clearance.

.

 

[petertha]

The simplified s & h formulas only apply when Vc & Vd are represented as cylindrical cans. A flat top piston meets this criteria & is easy to calculate. But many combustion chambers are not shaped like simple cylindrical cans in real life, so you have to get a handle on actual volume, either measured or computed, and compute CR on that basis. The combustion chamber could be domed or asymmetrically curved in cross section. Valve faces would be a flat surfaces, maybe semi-flush or maybe slightly submerged. Ignition plugs affect volume with clearance or protuberance. The piston top may not be a simple flat or match the head section profile entirely for various reasons. The higher the CR, the more sensitive even tiny dimensional changes to head features become. I seem to recall on certain RC engines, the difference in a glow plug washer thickness was worth 0.5 CR or thereabouts.

 

[Gedeon Spilett]

A function in 3D drawing software allows the calculation of a volume, hence it is easy to model the combustion chamber to determine its volume, even for a complex shape...more easy than measuring it with a liquid, particularly if the engine is not yet built!

 

[GreenTwin]

A function in 3D drawing software allows the calculation of a volume, hence it is easy to model the combustion chamber to determine its volume, even for a complex shape...more easy than measuring it with a liquid, particularly if the engine is not yet built!

I use the mass function in Solidworks to calculate the mass of various 3D parts, so I can calculate how much metal I will need to cast a part.
I can change the material to aluminum, bronze/brass, gray iron, etc.
This is very helpful in avoiding short pours, where your crucible does not hold enough metal to completely fill the mold.

The volume function is not something I thought about using.
There are a lot of features in 3D modeling programs that I don't use, but probably should be taking advantage of.

.

 

[GreenTwin]

There appears to be a recess in the top of a Detroit Diesel 671 piston, and both the two and four valve heads for the 671 appear to be flat on the surface facing the piston.
The injector appears to be directly centered in the cylinder.

.

 

[GreenTwin]

I just found out that the origins of the Detroit Diesel line of engines originated with GM's purchase of the Winton Company around about 1930.
Never knew that.
(not my drawing)

.

 

[DougB]

Hello, I would like to know if there is a formula to calculate what diameter and stroke a diesel engine should have with a compression ratio of 20 to 1 or with a compression value of 25 bars.

Hello Rubin,

It is reasonably easy to calculate the compression ratio using a pressure gauge.
Measure the max. pressure of the cylinder then divide by 14.7 atmospheric pressure
Example; cylinder pressure measured 80-PSI divide by 14.7 (Atmos. pressure), answer 5.4:1
Hope this is of assistance

Doug Baker
Scarborough WA

 

[peterl95124]

(once again...) "Compression Pressure" and "Compression Ratio" aka "Volume Ratio" are NOT the same, the "compression ratio" is purely geometric and does not take into account thermodynamics, the actual "Pressure" after "Compression" is given by a much more complicated formula (because so much work has been done to the gas during compression, and that work shows up as additional pressure and temperature)

in addition to PV/T = const, there are these formulas PV^gamma = const, TV^(gamma-1) = const, and P^(1-gamma)T^gamma = const, and the more useful for us formulas

PR = VR ^ (-gamma), and TR = VR^(1-gamma)

where PR is pressure ratio, TR is temperature ratio, VR is volume ratio.
and gamma = 1.4 for diatomic gases like air being mostly N2 and O2,

these formulas require using temperature measured relative to absolute zero, and pressure relative to a vacuum, but if you do all the necessary conversions you'll get these numbers

20:1 974-PSI 1296-degF (or 66 Bar, and 700-degC), for STP input (1 Bar, 20-C)


the main issue with homebuilt Diesel engines is that the injector pump has to both overcome the 66 Bar cylinder pressure, and apply an additional 66 Bar for spray atomization, so a total of ~130 Bar, or ~2000 PSI, is required. a non-trivial task ! (also 974-PSI applied to a 1" piston has about 750 pounds-force on it, think about how strong the con-rod has to be and how much force the crankpin and crankshaft bearings have to endure, then maybe double those numbers for after ignition).


(PS (once again...), the 700-degC is a temperature where ignition is guaranteed, the "flash point" or what ever else temperature you'll see on the internet for various fuels is totally irrelevant as it is a temperature below which it is guaranteed that ignition will NOT occur, and above which ignition only *might* occur, so it is a "safe handling" temperature, not a guaranteed ignition temperature)

 

[minh-thanh]

20:1 974-PSI 1296-degF (or 66 Bar, and 700-degC), for STP input (1 Bar, 20-C)

It is based on absolutely perfect conditions, which in reality are never achieved.

(PS (once again...), the 700-degC is a temperature where ignition is guaranteed, the "flash point" or what ever else temperature you'll see on the internet for various fuels is totally irrelevant as it is a temperature below which it is guaranteed that ignition will NOT occur, and above which ignition only *might* occur, so it is a "safe handling" temperature, not a guaranteed ignition temperature)

Flash point is different from auto ignition temperature !!!!