# How to calculate the amount of thrust of a autogyro during auto rotation?

When a autogyro/gyrocopter is in a horizontal steady flight the rotor should be able to provide enough thrust using the auto rotation principle if the horizontal speed can be regulated by the vertical propeller.

I was wondering how the amount of thrust provided by the main rotor of a autogyro during auto rotation can be calculated. All the characteristics of the autogyro and his blades are known.

The horizontal speed of the gyrocopter can be regulated by additional engines and they do not need a specification.

In auto-rotation, either flying level, or with a constant sink speed, the vertical component of the thrust provided by the rotor is exactly the same as the weight of the gyro...

In Wikipedia https://en.wikipedia.org/wiki/Disk_loading#Momentum_theory you can find the derivation of the following expression:

$T = 2v^2· A· rho$

where T is the thrust of the rotor, v the sink speed in vertical auto-rotation, A the 'disk area' (that swept by the blades) and rho the air density.

• Thanks for you answer! I understand that the in steady horizontal flight the thrust is equal to the weight but how can it be calculated. For the formula that you provided a sink speed is necessary, but in this case the sink speed is zero. At least as you specify it as the speed at which the plane is moving down. That is the part I'm struggling with as I can't seem to understand how this v can be obtained for an auto-gyro in auto rotation at a steady horizontal flight. – Rudy Sep 26 '17 at 11:56
• It's always he vertical component of the thrust... It's an important detail, because the disk is more or less tilted backwards, except when the gyro is descending in vertical autorotation. Concerning your doubt regarding v, just imagine the case of vertical autorotation, calculate T for it and use it, correcting for disk tilt, for the case of s/l flight. Now, you don't know the disk tilt, but for high horizontal gyro speeds, that tilt is almost irrelevant... – xxavier Sep 26 '17 at 12:01
• What do you mean by s/l flight? And if I understand you correct v for horizontal flight is almost equal to v in vertical flight (correcting for the tilt)? There is no possibility to calculate v using the speed at which the gyro is flying and how much the disk is tilted? I'm most interested in a relation between the horizontal speed and the amount of thrust. – Rudy Sep 26 '17 at 12:19
• By s/l I mean straight and level. The thrust required from the rotor is larger at smaller speeds, because the tilt is higher. I don't know now where to find the value of that tilt as a function of speed, weight, etc. but somewhere in the internet I'm sure you can find it... Ask in the Rotary Wing Forum, for example... – xxavier Sep 26 '17 at 12:26

The rotor of an Autogyro does NOT provide Thrust, it provides Drag. This is what differentiates Autogyros from Helicopters, and is why an Autogyro needs a separate engine-driven propeller. So the question needs clarifying as to what you actually want.

• Both helicopters and autogyros are kept airborne by the upward thrust generated by their rotors. In the helicopter, the rotor is directly driven by the engine, and its plane can be tilted forward, so that the aircraft may also move forward... In the autogyro, the rotor is indirectly driven by the engine, via a pneumatic/autorotation transmission, and in forward course, the disk is more or less tilted backwards, the horizontal motion being achieved by the thrust of the prop. – xxavier Sep 26 '17 at 12:19
• @xxavier the upward thrust generated by their rotors I think the phrase "upward thrust" is confusing. In fixed wing thrust is considered a horizontal component in level flight. Is the term used differently with rotorcraft? – TomMcW Sep 26 '17 at 17:06
• @TomMcW I don't think it's confusing. Rotors and propellers are essentially the same thing, and they both provide thrust... – xxavier Sep 26 '17 at 19:49
• @xxavier I would say a propeller provides thrust whereas a rotor primarily provides lift. Propellers are using the same principle as wings, but we don't usually refer to it as "lift" because of the direction. I understand what the op is asking, but when I first read the question I thought the same thing: the rotor doesn't provide thrust at all, only lift and drag – TomMcW Sep 26 '17 at 19:53
• @TomMcW All right, you would say it that way, so let it be... – xxavier Sep 26 '17 at 20:04