# How would we calculate the load factor on an aerial vehicle while landing due to sudden gust loads?

In order to design the landing gear (wheels and suspension) of our model Airship, [say "m" kg -expected mass], I wanted to know, is there any way to calculate the loads which might be experienced by the wheels on impact with the ground (taking into consideration the unexpected gust loads - with gust velocity downwards say "V-gust")•

For simplicity I am Modelling it as a rigid body for now.

Note:- I thought of one way to calculate it, using momentum transfer.

Rate of change of Momentum = Force = density(rho) x projected Area(A) x (V-gust)^2.

Hence,( Gust force + Weight -Buoyant Force) ÷ Mass (m) will give me resultant acceleration.

Q1. Is this a right approach to calculate load? Q2. Even if it's right, is this the load the wheels will experience during impact?

Please help me clear my confusion.

Edit:- Basically I want my designed landing gear with a normal sink speed upto 3m/s to be able to endure the landing impact even in case of an additional vertical downward gust upto 10m/s at the moment of touching the ground. This is as specific and clear I could get.

• Q1 No, see Gurkans answer. Q2 No, see Peter's answer. The problem with downwards gusts is the mostly the added velocity of the ship, not the pressure due to downwards gusts. Also realize that the wind 'has to go somewhere', so close to the ground, pure vertical gusts are almost impossible, and instead they 'spread out' to a horizontal velocity. – Sanchises Jun 11 '15 at 7:56

## 2 Answers

You need at least the stroke of the tire-gear combination to calculate a load. If the airship contacts the ground with a velocity of $w$ and a mass of $m$, the impulse $m\cdot w$ needs to be absorbed by a force $F$ acting along the stroke $s$, as in $m\cdot w = F\cdot s$. Adding airship flexibility will greatly improve the accuracy of the result, because I suspect the hull will deform easily and add to the stroke.

If you need an example of how this is calculated for a Boeing 747, please click here.

• I am sorry, i didn't understand. Why should we calculate stroke length first to calculate force, plus thats also a problem how do i calculate the resultant velocity during impact because i dont think that the velocity of vertical gust will become velocity of airship. I thought calculating acceleration would be more feasible. – Manish Jun 10 '15 at 2:24
• @Manish: Your question is sufficiently vague, and gusts don't blow into or out of the ground. So the gust speed is less important than the sink speed of the airship. To absorb energy, some force has to do work along a distance. The force is the gear load, and the distance is the stroke. And if you don't know the sink speed of the airship, you have no chance to calculate the gear force. – Peter Kämpf Jun 10 '15 at 6:33
• @Manish Think of it like this: Gust leads to an increased downwards velocity (sink speed), leads to an increased momentum that should be absorbed over a stroke $s$, which leads to an increased force. Always think action->reaction, don't just multiply all quantities you have until the units match up. – Sanchises Jun 10 '15 at 15:55
• @peter I do know my max. Sink speed and yes gusts definitely don't come from the ground rather i was mentioning the vertical gusts above the airship pushing it further faster downwards. And thats what my doubt is, if I dont know both force and stroke length how to proceed To calculate them. Is it a standard way to assume the stroke length? – Manish Jun 10 '15 at 17:35
• @Sanchises What you wrote is exactly what i am asking to calculate, the reaction force. And I don't think i am blindly multiplying quantities. RhoAv^2 is a common way to calculate force due rate of change of momentum. I am asking if its practical to apply. – Manish Jun 10 '15 at 17:41

If the question is about calculating the aerodynamic load acting on an airship, the answer is independent of the flight condition: whether it's landing, before touchdown, or after touchdown.

The aerodynamic load around the airship due to any gust, depends on the shape of the airship. Simply stated, the additional force due to gust would be: "CD * Ref_Area * V_gust"

This emprical formula gives a force, that must be reacted by the landing gears. However, note that, the main assumption is this: the gust is a steady airflow which is comparably larger than your Airship. In contrast, if the Airship is quite large, then the gust would probably affect only some local portion of the vehicle.

• Yes the airship will be quite large. But i do not want drag, i am concerned about maximum load which the tyres might face in case of presence of any vertical gusts. – Manish Jun 10 '15 at 2:20
• My answer is more applicable to small airships (<20m size). As size increases, the airflow will be more difficult to predict, and assumptions will not be as valid. Btw, vertical gusts do not occur that much when near the ground (they do occur at the center of wind shears, but otherwise they would be comparably slower than lateral gusts). – Gürkan Çetin Jun 10 '15 at 18:42