Parachute area, Growth in: Flat circular versus Ringslot

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MetricRocketeer

MetricRocketeer

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Hi everyone,

I just electronically received my Peak of Flight newsletter (issue #485), which pertains to parachutes.

The author writes this on page 2:

"... the growth in parachute area during inflation of a ringslot parachute area is more even (a linear function with time) than that of a flat circular parachute where not much happens at the beginning of the inflation sequence but towards the end ... wham ... it is open (a power function with time)."

Could someone please tell me what the two different equations would be for the growth in parachute area.

So, I am asking for the linear function and for the power function.

Thank you.

Stanley
 
I will try to provide this info to the best of my knowledge. Since the ring slot area increase is linear, we can use the fill time equation and make it a function of diameter. I can't remember where I saw the polished equation for area as a function of time.

The solid, flat chute equation is the standard area as a function of time equation.

I hope this helps and any input, corrections or references are greatly appreciated.

The main reference is Knacke.
 

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Hi Benjamin,

Thank you for your reply.

Let me see.

The basic formula for a linear function is f(x) = a + b*x. If we are dealing with a function of time, then I should write f(t) = a + b*t. But if the area is a function of radius, then we would have A(r) = pi * r^2. For the linear portion, I should write r(t) = a + b*t. I would then compose the function to get A(r(t)) = pi * r^2. In that case, however, the area would not be increasing linearly. In that case, the area would be increasing quadratically. So I am confused there.

Second, the basic formula for a power function is is f(x) = a*x^b. Again, I could write f(t) = a*t^b. So in this case, what does a and what does b equal? I need to know the parameters.

Thank you, or anyone else.

Stanley
 
You are correct on the first one. I will have to dig back through my references to find the exact equation. It would have to be something to the effect of:

F(A)=(n*A)/V
n=inflation constant, non dimensional
A=area
V=velocity

I honestly have never worried about the increase in area vs time because I am lazy and use the inflation time formulas to predict forces and I have never designed a high speed deployed ringslot. But if I can't find it I will ask a "parachute god" for the reference

The second is
a=1
b=2
t is the variable
n is the ratio of the projected starting area to the full area and is the output
 
BAMA_Recovery_Systems said:
You are correct on the first one. I will have to dig back through my references to find the exact equation. It would have to be something to the effect of:

F(A)=(n*A)/V
n=inflation constant, non dimensional
A=area
V=velocity

I honestly have never worried about the increase in area vs time because I am lazy and use the inflation time formulas to predict forces and I have never designed a high speed deployed ringslot. But if I can't find it I will ask a "parachute god" for the reference
Click to expand...
Thank you for your reply.

I wouldn't mind having the exact linear equation, if that is no big trouble for you.
BAMA_Recovery_Systems said:
The second is
a=1
b=2
t is the variable
n is the ratio of the projected starting area to the full area and is the output
Click to expand...
The power equation is the one that particularly interests me. I would like to use this as an example for the courses I teach in college algebra and in statistics.

The problem is that I am still unclear on the specifics.

Let us use a realistic example for model rocketry. Let's say that we have a flat-circular parachute that, when fully unfolded, measures 30 cm in diameter and thus has an area of 706.9 cm^2 to the nearest tenth of a centimeter. So at time_sub_0, before the parachute has deployed at all, its area equals zero (right?). Once the parachute has fully unfolded, its area measures 706.9 cm^2.

Here is what I would very much like to have, please. I would like to have several intermediate measurements equally spaced in time, and the exact power equation that was used to generate those measurements.

I would be most grateful for this, if you please.

Thank you.

Stanley
 
MetricRocketeer said:
Thank you for your reply.

I wouldn't mind having the exact linear equation, if that is no big trouble for you.

The power equation is the one that particularly interests me. I would like to use this as an example for the courses I teach in college algebra and in statistics.

The problem is that I am still unclear on the specifics.

Let us use a realistic example for model rocketry. Let's say that we have a flat-circular parachute that, when fully unfolded, measures 30 cm in diameter and thus has an area of 706.9 cm^2 to the nearest tenth of a centimeter. So at time_sub_0, before the parachute has deployed at all, its area equals zero (right?). Once the parachute has fully unfolded, its area measures 706.9 cm^2.

Here is what I would very much like to have, please. I would like to have several intermediate measurements equally spaced in time, and the exact power equation that was used to generate those measurements.

I would be most grateful for this, if you please.

Thank you.

Stanley
Click to expand...

I will try to get all of this info for you in the next day or two. If you want I can also send you a few references so that you can look over the context of the equations. Do you want it in a spreadsheet or just written/ typed out?
 

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