Stroke and Bore of a Piston

Date: 05/11/2000 at 01:21:40
From: Frank Walsh
Subject: Stroke and bore of a piston

A double-acting diesel engine for a ship has eight cylinders with bore 
1 m and stroke 1.3 m. The piston-rod diameter is 150 mm.

Determine:

a) The capacity of the engine.

b) The distance between the top face of the piston and the top of the 
cylinder head in the Top Dead Center (TDC) position, and the distance 
between the bottom face of the piston and the bottom of the cylinder 
in the Bottom Dead Center (BDC) position for a compression ratio of 
18:1 on both sides of the piston. Assume the compression starts at the 
extreme stroke positions and that the piston and cylinder heads are 
flat.

Answers: a) 16.15 m^3
         b) 76.5 mm, 74.8 mm

These are the answers in the book but it doesn't show how to work them 
out. I'm really stuck!

Thanks a million.

Date: 05/11/2000 at 05:45:06
From: Doctor Mitteldorf
Subject: Re: Stroke and bore of a piston

a) The capacity is the displaced volume, pi*R^2 times the stroke. 
Multiply by 8 for 8 cylinders. But the "double-acting diesel" gets 
power from both sides of the piston, so you get to almost double this, 
but not quite because the piston-rod takes up some volume. The 
effective area on one side is really pi*R^2, but on the other side 
it's pi*(R^2-r^2), where r is the piston rod radius = .075 m.

b) The minimum distance to the top and the maximum distance to the top 
must be in the ratio 18 to 1, and their difference must be the stroke, 
which is 1.3 m. A little algebra gives you the min and max. This gives 
the 76.5 mm answer. For the other side of the cylinder, where the 
effective bore area is reduced by the area of the piston-rod, they've 
reduced this by the ratio (bore-rod)/(total bore area). I can't 
imagine why they've done this.

- Doctor Mitteldorf, The Math Forum
  http://mathforum.org/dr.math/