*The following article has been written by Manuel Schütz after the Autorotation discussion on twobladers came up.*

* The ideas and concepts explained are revealing, but the open questions as well. The full article is available for downloading in the button at the end of the excerpt.*

**Excerpt**

## 1 Acknowledgements

In the late 1990’s I received and wrote many letters from/to Georgi Dimantchev. I didn’t understand anything about his achievements in boomerang aerodynamics since it’s such a subtile topic and the impacts on MTA flights are hard to see. My apologies here if you read and see nothing but questionmarks. It’s a difficult task to write about such a complex subject in a foreign language. Hopefully some of the information is useful. To really understand why the

sinking speed is proportional to the square root of the wing loading I needed to go through the entire calculations which is documented as well.

It took me roughly 20 years to have an idea of how far his considerations about the aerodynamics at low Re-numbers have gone! My article doesn’t focus on that, my goal is to understand the dynamics of a hovering MTA boomerang when the aerodynamic coefficients are known.

I will forget many important names, my apologies for that! Certainly I need to mention Ted Bailey, Wilhelm Bretfeld (when I bought my first books I read their names on the plans). Ted Bayleys tuning advides have been valid to now and in my article I haven’t found anything new, but I understand better why the tuning (I prefer to say twist) has to be as proposed by Ted Bailey.

Axel Heckner was and is an inspiration for me not only for MTA boomerangs. His first attempts to make a threeblader fly more than 25s in New Zealand (1996) have changed my view to MTA boomerangs. At the same time I saw the Japanese team throwing symmetric threebladers with excellent stability but less flight time than Axel’s threeblader. Back to Georgi: After many experiments I found that the 1. choice of the correct airfoil is more

important than I thought for the stability and 2. that a not-looking-promising airfoil can be a good choice. For example close to symmetric airfoils for MTA-threebladers with rather blunt leading edges. I still have all of these letters and keep studying them.

Without Jonas Romblad I would never have started to make my own composite MTAs! He lifted all the secrets behind his legendary MTA-boomerangs, the value of his advices on how to make a mold cannot be estimated high enough!

As said, in the present article the topic is the dynamics and kinematics of hovering MTAs.

## 2 Introduction

Many of the boomerang throwers may have asked themselves: How on earth is it possible thatan MTA stays in endless autorotation even with positively twisted wings (leading edge up)?

From experience we know that a positive twist generates more lift but also more drag. Hence

the boomerang should gradually lose spin. We know that boomerangs keep autorotating as long as you don’t twist the wings too positive (nose up). But why is this? I answer this question using the blade element theory. Additionally

I tackle the question if it is necessary to construct an MTA such that it starts to spin when just dropped without any initial speed and spin. We know this behaviour from maple- or samara seeds. I found that this is not a necessary condition! In general an MTA with positive twist doesn’t start to spin on it’s own, but it maintains it’s spin when starting it’s hover with a certain spin.

A common misconception concerns the mass: I show that it’s not true that the sinking speed of a boomerang is proportional to it’s mass. I found: To double the sinking speed you need to quadruple the mass. And a second misconception regarding the quality of MTA-boomerangs: It is of no significance how many 1,2,3…10min flights an MTA has done unless it happened in either dead calm conditions or laminar wind on a beach. Don’t cheat yourself: Test your MTA’s in thermal-free conditions whenever possible to estimate the potential of your boomerangs! I even once saw one of my balsa cross stick rise up into the sky and disappearing!

Example for useful data:

Thrown 10 times, average time 35s, lowest 30s, highest 40s. Not useful: 4.11.2007, 1 min 32s. Blade element theory, a suitably tool for this topic, has earlier been applied by John Vassberg (”Boomerang flight dynamics, aerodynamics lecture, 30th AIAA Conference, New Orleans, Louisiana, 28.June 2012”) for circular boomerang flights with the elementary finding that for circular flight paths the range is not only independent of the boomerang mass, but also independent on the layover at the throw.

In my investigation I assume a laterally stable hover with just a descent speed in negative z-direction. In steady state hover, the sum of all forces and all torques is zero. It is important to analyze if a steady state hover is stable. That means: If something disturbs the spin of the boomerang, does the spin recover to the value before? Generally it does, but not if a big part of the boomerang is in stall.

Aerodynamic forces of a wing/blade with surface S are calculated as

Re being the Reynolds number 0 < Re < 50000. I use lift/drag coefficients calculated with XFOIL.**Definition of α:** Every airfoil can be blown from a direction which leads to zero lift. If the airfoil is symmetric (such as long distance boomerang airfoils) that direction equals the chord line (”leading edge to trailing edge”). If the airfoil is cambered (such as an MTA airfoil) it creates lift if blown along the chord line! So in my language MTAs have a ”twist” even if their bottom is completely flat.