How much thrust is lost through a curved exhaust nozzle?

In modern VTOL aircraft energy is usually directed through nozzles to achieve vertical lift. How much energy is lost when changing the direction of flow in static thrust conditions?

• Reminds me of that Mythbusters episode where they bent the barrel of a rifle 90 degrees and it was still lethal. One of my favorites! ðŸ™‚ Aug 28, 2020 at 0:24
• Note that the Rolls-Royce Pegasus always forces the exhaust around a bend, no matter which direction the nozzle points... Aug 28, 2020 at 11:08
• My naive thought would be that the direction of the vectoring force (the "bending" force) is in this case upwards (remember those rotating lawn sprinklers using some of the water pressure to propel their rotation) which means that not too much power would be lost to the vectoring, only rather small amount to increased friction/compression in the bend. Aug 28, 2020 at 12:23

For the F135 engine in this photo, thrust in hover is only about one per cent less than maximum thrust, if Pratt & Whitney's data sheet is to be believed.

Maximum Thrust Class 41,000 lbs
...
Hover Thrust 40,650 lbs

The Hawker Harrier's maximum thrust was about 20,280 pounds. An approximation of its maximum vertical thrust at low airspeed is given by its maximum vertical landing weight, 19,918 pounds, again just about one per cent less.

• Thanks for the info and the links! On the F135 it lists the lift fan as part of the hover thrust so it's hard to know for sure as the engine splits it's maximum 27000 lb thrust (military power). 18,680 lbs of thrust comes directly from the rear nozzle. Something like 8320 lbs worth of thrust is sacrificed to drive the more efficient lift fan which then provides once again 18,680 lbs. Aug 27, 2020 at 23:11
• The trick seems to be to constrict the flow at the nozzle enough that the effects of the 90 degree bend on the flow are minimized. In effect it is like blowing up a crooked balloon and comparing its "thrust" to a perfectly round one. The flow at the bend is much slower than at the nozzle. Aug 28, 2020 at 1:32
• "a few percent"? Based on those numbers, the loss is 0.86% for the F135 , so "a fraction of a percent" would be more accurate. (It's a 1.79% loss for the Harrier, so I'll cut you slack on that one.) :D Aug 28, 2020 at 18:16
• Damn I sure love the F135 engine. Dec 23, 2022 at 22:55

A 90 degree bend in a pipe where the radius of the bend is of order ~one pipe diameter creates the same pressure drop as a length of that same pipe of order ~ten to fifteen times the pipe diameter.

• Which is how much, compared to an unmodified pipe? Five per cent? Fifty per cent? Aug 27, 2020 at 18:03
• do not know in terms of percent. Aug 27, 2020 at 21:24

There is very little duct loss due to the double 90 degree bend in the exhaust. Hawker chief designer Sidney Camm used a similar design in the Hawker Seahawk a 1950s Naval fighter, which had twin exhausts exiting behind the trailing edge wing root. Camm found this arrangement had lower duct losses than a long duct exiting under the tail. This was an important consideration given the limited power available from early jet engines. Camm used the same duct arrangement on the Hawker Kestrel / Harrier, working closely with Stanley Hooker, chief engineer from Bristol engines (later merged with Rolls-Royce) who developed the Pegasus.

• Hi! Do you have any public sources you could like for those that would like to know more? Dec 23, 2022 at 10:36
• Hi, take a look at Stanley Hookersâ€™ brilliant autobiography called â€˜Not Much of an Enginneerâ€™. He writes about the design of the Pegasus engine as well as working with Sidney Camm. Dec 23, 2022 at 13:26
• That book is online. Which pages mention the Hawker Seahawk ducting? Dec 23, 2022 at 18:34