# Reply To: Porta's Derivation of Lempor Theory

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#5095
John Hind
Participant

Hi Martin – have you a copy of Jos Koopman’s book ‘The fire burns much better….’?

The book is useful in that lists and critiques the history of exhaust system development over the last 200 years. It also includes the various formula derived over the years for describing mathematically the workings of exhausts systems. It also includes the formulae derived by his PhD Supervisor – Dr Robin Saunders.

In the book he praises the Lempor Exhaust but like yourself is sceptical aboout the formula and points out a transcription error on the versions available on the web – if my memory is right a plus should be a minus or vice versa in one of the terms. He also reverse engineers the equation and concludes that it is the same as one developed by Zeuner in the 1850’s.

I used the equation, but put in realistic values for inlet loss and for diffuser performance taking into account diffuser geometry and correcting the transcription error. I developed a spreadsheet using the corrected equation and then developed graphs of draught for different steam rates. The graphs showed decreasing vaccuum for increasing steam and gas flow rates which is contrary to what is seen in real life. So I am sceptical of the equation and given time would like to use the same input data into other equations and see what the results are.

Others have used the equation and developed succesful exhausts, see this website

http://home.ca.inter.net/~mguy/A%20Lempor%20Exhaust.htm

There is a link in it to a Excel based calculator developed from the Porta Equation.

Despite our scepticism about the equation others have developed succesful Lempor exhausts. The Lempor we fitted to S160 has achieved its objectives of turning a poorly steaming engine in a better steaming one, which uses less coal than it did before. We had a one off chance to measure vacuum on it back in early 2017. We are in the course of doing similar measurements on a similar engine of the same class on another railway. To do these tests we are in the hands of the railway so progress is slow depending on locomotive availability and access to run trains.

The experience we have had with Lempor Exhausts is simlar to others who have fitted Lempor Exhausts, so despite the equation the Lempor Exhaust does work.