# How does this total energy compensation pitot tube work?

This is a pitot tube I saw on a glider:

The far right end plugs into a receiver. The far left end has the RAM port at the tip, the static ports just behind it, drilled in laterally, and a venturi hanging down below.

There's some kind of what looks like acid etching on the tip, terminating just behind the static ports.

Something similar can be seen at https://www.esa-systems.com/en/products/details/total-energy-probe-brst-840-mm-1/, where they mention "The TE – measuring head is based on the long established Venturi nozzle principle."

From other things I've read, I had the understanding that TEC calculations required a pressure measurement in the lee of a round surface. This seems to be a little different here. How is this probe working? What does the venturi do?

P.S. I'd love a mathematical description.

The pitot tube here does not do anything special- it's simply a pitot tube, static port, and venturi all combined in one instrument. It delivers these three pressures to the pressure instruments from three separate ports. The part that plugs into the aircraft looks something like this:

From there, the pressures can be used to drive a normal airspeed indicator, total energy compensated variometer, or any other pressure instruments.

The excellent answer here describes how a backwards-facing pitot probe can be used to make a total energy measurement. Facing a pitot tube backwards negates the value of the measured pressure- it turns $$\frac{1}{2}\rho v^2$$ into $$-\frac{1}{2}\rho v^2$$, i.e. a suction. It just so happens that a venturi tube also creates a suction proportional to $$\rho v^2$$, so a venturi tube can be used in lieu of a backwards facing pitot tube to accomplish the same measurement.

Specifically, the pressure in drop in a venturi tube is given by $$P_s-P_v=\frac{\rho}{2}(v_2^2-v_1^2)$$, where $$v_1$$ is the true airspeed and $$v_2$$ is the speed of the air in the venturi tube. $$P_s$$ is the pressure at the opening (i.e. the static pressure) and $$P_v$$ is the pressure as measured by the venturi tube.

Assuming incompressible flow (which is a good approximation for so long as the flow is sufficiently subsonic), $$A_2v_2=A_1v_1$$, where $$A_1$$ and $$A_2$$ denote the cross-sectional areas of the mouth of the venturi and its narrowest point, respectively.

Putting this together, the venturi pressure is given by:

$$P_v = P_s - \frac{\rho v_1^2}{2}\left(\frac{A_1^2}{A_2^2}-1\right)$$

If $$A_1/A_2$$ is chosen to be $$\sqrt2$$, this equation is identical to the one in the linked answer, and so works identically to a backwards-facing pitot tube in measuring total energy.

• Neat. Do you happen to know the relative advantages of using a venturi vs. a backwards ram tube? And why does the OD of the venturi flare out in the pictured probe? Jul 16 at 23:31
• @KennSebesta One obvious advantage is that reduces the total number of tubes needed, and it can be placed in relatively undisturbed air. Obviously, it's impossible to place anything backwards facing in totally undisturbed air. Jul 16 at 23:46
• I'm not 100% sure why the lip flares out, but my guess is that a sharp edge would create interference and disturb the measurement. Jul 16 at 23:49