How does one determine the freestream and ultimate slipstream velocities to estimate thrust?

The task before me is estimating the thrust of a propulsion system (a ducted fan) using this equation for thrust (Eq. 2.1.1)1:

$$T = (mass\; flow\; rate)\;(slipstream\; velocity - freestream\; velocity)$$

I know what the ideal inlet and exit velocities of the system are, but how does one determine the freestream and slipsteam velocities so that estimated thrust may be calculated?

1 Warren F. Phillips, Mechanics Of Flight Second Edition, John Wiley & Sons, Inc., Hoboken, New Jersey, 2010, p.153

1 Answer

The free stream velocity can be measured with a calibrated air data system. This uses a pitot tube somewhere at the front, the readings of which have been compared to known speeds in previous flights. The difference between the total pressure and the static pressure gives the dynamic pressure which can be translated into the desired speed.

The speed in the slipstream must be measured across the full cross section to ensure that the full speed profile is known so the slipstream speed used for thrust calculation really is the mean of all the speeds in the slipstream. This is done by measuring the total pressure at several locations, for example by using a moveable rake.

Combined temperature and pressure rake (picture source)

• Thanks, Peter. It occurred to me that I could also check the text I cited for "freestream velocity". Dec 4 '16 at 16:27
• If I had, I would have seen on the second page of the text: "...V<sub>∞</sub> is the freestream velocity or <i>relative wind</i> far from the body...". So, for estimating static thrust, I could use zero. Dec 4 '16 at 17:10
• @DavidWalden: That is correct, however, some formulas put the free stream velocity in the denominator, so setting this to zero might not always be the easy solution it seems. Dec 4 '16 at 20:27