# Smeaton's coefficient

The Smeaton coefficient , named after John Smeaton , describes the relationship between pressure and aerodynamic resistance of a body in a gas flow. However, the dynamic pressure of the medium is not taken into account.

• ${\ displaystyle D}$Air resistance in lbs
• ${\ displaystyle V}$Speed ​​in mph
• ${\ displaystyle A}$Area in square feet
• ${\ displaystyle C _ {\ mathrm {D}}}$ Drag coefficient (for the reference environment = 1). Corresponds to today's value${\ displaystyle c _ {\ mathrm {w}}}$

The resistance equation

${\ displaystyle D = k \ cdot C _ {\ mathrm {D}} \ cdot V ^ {2} \ cdot A}$

gives k for the Smeaton coefficient

${\ displaystyle k = {D \ over C _ {\ mathrm {D}} \ cdot V ^ {2} \ cdot A} {\ mathrm {lbs \ over mph ^ {2} ft ^ {2}}}}$

In 1759, Smeaton gave in his work An Experimental Inquiry Concerning the Natural Powers of Water and Wind to Turn Mills and Other Machines Depending on Circular Motion a value of k = 0.005.

Up to about 1900, after further experiments, the value k was found to have a scatter of 0.0027 to 0.005. The Wright brothers trusted the value of k = 0.005 and initially built two gliders, but they did not fly. Extensive experiments then resulted in a value of k = 0.0033, which corresponded to the current value of k = 0.00327 with sufficient accuracy.

Because of its limited usefulness, the Smeaton coefficient has not been used since around 1920. Instead, the Bernoulli equation was used.

## Individual evidence

1. ^ A b John David Anderson: A History of Aerodynamics: And Its Impact on Flying Machines . Cambridge University Press, 1998, ISBN 978-0-521-66955-9 , pp. 58.313 f . ( limited preview in Google Book search).