Coning is a simplified helicopter rotor blade model to visually see the effect of rotor speed, lift, blade length and weight on the coning of the blades. This app can help with training in the classroom both in demonstration to show specific effects and also for students to experiment hands-on to gain familiarity with some of the variables that make up the complex nature of rotary flight. Please note that to keep things from getting over-complex this model is for a stationary helicopter with no wind, so does not include any dynamic blade flapping or other cyclic variable movements.
The model shows a single blade with its root at the left. The blade is in 3 sections: 1) A rigid strut at the root. The length of this strut is controlled by the r slider and is in metres. 2) A middle section which generates lift. It is modelled as having an evenly distributed mass along its length. The length (in metres) of this section is controlled by the b slider and the total mass (in Kg) by the blade mass slider. The lift along the blade is set with the 3 lift sliders. The lift factor is an arbitrary proportionality factor (per unit length) and is set at the left end (root), middle and right end (tip). A quadratic curve is fitted to these three values and a graph of how the lift proportion varies along the length of the blade is shown at the bottom of the screen. 3) At the tip end is a light string with a tip weight at the end. The length of this string is controlled by the s slider (in metres) and the Tip mass slider controls the weight at the end of this string (in Kg).
The Bits slider controls how many segments the blade is split up in to during the modelling calculations. Leave this at 1024, but by moving it down you can get a feel that no improvement would be gained by splitting it into more than 1024 sections. Finally, set the RPM of the blade with the blade RPM slider.
The picture in the centre of the screen shows the modelled shape of the blade with the given parameters; effectively viewed side on in a physical sense. The readouts above the picture are as follows:
Base angle: Is the angel (in degrees) that the root of the blade (mid section) makes with the horizontal. This effectively is the direction of the force holding the helicopter up.
Base T: Is the tension (in Newtons) at the root of the blade. Combined with the Base angle you can calculate the upward Lift force the blade is giving (transferred through the root of the blade).
Generated Lift: simply combines the Base tension and Base angle to give the total vertical lift effect. Not to be muddled up with:
Lift eff: Is Lift effort - the total lift generated along the length of the blade. Due to coning, not all this lift will be directed vertically upwards, but it will give an indication of the drag that must be overcome and therefore the power required.
Lift efficiency: gives the Generated Lift as a percentage of Lift effort; effectively the percentage efficiency of converting the left effort into true vertical lift. The more the blades cone the less efficient the Lift effort is (because lift isnt directed vertically upwards), but adding more mass to the blade and tip to prevent coning also counteracts generated lift with added weight so also reduces efficiency. A balance between the two is required.
Max ht: Is the maximum height (in metres) the blade reaches vertically, compared to the height of the blade at the root.
Disclaimer: Whilst interesting to see and play with, the modelling used makes many simplified assumptions, completely ignores drag effects and any airflow or flapping and the mathematics has not been checked by a 2nd person. It accordingly should not be used to make real predictions and no liability is accepted for any use of these outputs. If interested, please contact the author to request the mathematical modelling behind this App so that you can verify its accuracy and understand its simplifications and limitations yourself.