Airplane takeoff speed

• Towely
In summary, the minimum takeoff speed for a light aircraft with a mass of 2.0x10^3 kg and wingspan area of 10.0m^2 is given by the equation V1= square root of ((2Fw)/(pA(((d2/d1)^2)-1)), where p is the density of the fluid (in this case, air) and d2 is the longer length of the wings. This equation takes into account Bernouilli's equation for ideal fluids and the need for a total force greater than the weight of the aircraft to achieve lift. However, it is important to note that this equation is not found in the textbook and the student faced difficulties in understanding it due to a

Towely

1. A light aircraft has a mass of 2.0x10^3 kg, a wingspan area of 10.0m^2, an upper wing distance of 1.75m, and a lower wing distance of 1.00m. What minimum takeoff speed must the airplane travel to become airborne?

2. V1= square root of ((2Fw)/(pA(((d2/d1)^2)-1))

3. How am I supposed to find p and Fw? Which length is d1 and which is d2?

Look at the ratio of d2/d1 and its effect on take off velocity V. Should V decrease as d2/d1 increases? If so then d2 is the longer length. Also d2/d1 > 1, because one does not want to be taking the sqrt of a negative number (argument) in this case.

Isn't there some discussion of the variables and the equation from the source (text) where the equation was taken?

Astronuc said:
Look at the ratio of d2/d1 and its effect on take off velocity V. Should V decrease as d2/d1 increases? If so then d2 is the longer length. Also d2/d1 > 1, because one does not want to be taking the sqrt of a negative number (argument) in this case.

Isn't there some discussion of the variables and the equation from the source (text) where the equation was taken?

No, it isn't taken out of the textbook. I read through multiple chapters a few times and haven't even found that equation in the book. I was gone the day he went through it too and he told me to ask one of my students for help because there's no time for us to meet outside of class. Every student I asked gave the reply "I just got the answeres from x." So I ask x how to do it. "Oh I just stole y's answers."

None of them could help explain it.

edit: Thank you for the answer about d2/d1. I am almost posative you are correct(and now that I look at it I feel silly for having to ask that question lol...) I gtg eat but I'm going to try and figure it out again, will post the results and how I got them within the hour.

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p is sapposed to be density correct? but how am I sapposed to figure out density from the given information if I can only figure out the volume of the wing and not the entire plane and only the mass of the entire plane is given?

And why would density matter in the first place?

Towely, you can use Bernouilli's equation for ideal fluids (even though air, strictly speaking isn't an ideal fluid) and you also have to take into account that the total force which is "pulling" the jet up must be greater than its weight. I hope that cleared things up a bit. :)

Hint: pressure = force/ wingspan area , also remember that you have TWO wings.