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Time To Accelerate To Maximum Velocity Including Drag

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Say I have an aircraft. I know it's thrust and the properties needed to determine its drag. The craft accelerates at at 10 m/s^2. Making the drag equal to the thrust, I determine its max speed to be 180 m/s. If I were to ignore drag, I could simply say it would take 18 seconds to reach maximum velocity, but I am attempting to determine how long it would take to reach 180 m/s including drag. As the velocity increases, the drag force with increase exponentially, so the net thrust/rate of acceleration would decrease each second. Is there a way to wrap F=ma with F=(CApv^2)/2 to determine the time to reach maximum velocity including drag or do I need to learn some calculus for this one?

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Why have you taken my formula? That formula pretty much explains dark matter.

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• 4 weeks later...

Why have you taken my formula? That formula pretty much explains dark matter.

The drag equation: F= pv2CDA/2, is his and it has nothing to do with dark matter.

Edited by OceanBreeze
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• 1 year later...

Do you need "thrust" to attain maximum velocity? Will inertia get you there?

Like the inertia of a foot launched, "flex wing" Hang Glider aircraft, which perfectly uses gravity, incline, and penetration among other things, to fly at its' maximum velocity (unknown).  The Hang Glider Wing has a human pilot, let's say he weighs 180 lbs, attached to the C/G by a harness, (which is the only connection to the wing) and let's say the glider weighs 60 lbs. In the air, the L/D in relative wind, determines it's velocity.  Would there be a formula (does the "drag equation" apply?) to find the maximum velocity and time, of such an aircraft in flight, considering that it may be one of the most perfect flying "machines" ever built.  No "thrust", no moving parts to speak of, no ailerons, no rudder, just weight shift under the C/G, and it flies perfectly. As far as maximum velocity and time goes, a pilot named John Heiney has performed 50 full loops in his king post Hang Glider, reaching speeds in excess of 90 mph to do it.

This week is the anniversary of the Wright Brothers flights in their gliders, which I believe led to the king post hang gliders of today, the geometry is basically the same.

Just for fun, here is a video of some bowsprit king post Hang Gliders, using gravity, incline and penetration to attain velocity.

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16 hours ago, Munch12 said:

Do you need "thrust" to attain maximum velocity? Will inertia get you there?

Like the inertia of a foot launched, "flex wing" Hang Glider aircraft, which perfectly uses gravity, incline, and penetration among other things, to fly at its' maximum velocity (unknown).  The Hang Glider Wing has a human pilot, let's say he weighs 180 lbs, attached to the C/G by a harness, (which is the only connection to the wing) and let's say the glider weighs 60 lbs. In the air, the L/D in relative wind, determines it's velocity.  Would there be a formula (does the "drag equation" apply?) to find the maximum velocity and time, of such an aircraft in flight, considering that it may be one of the most perfect flying "machines" ever built.  No "thrust", no moving parts to speak of, no ailerons, no rudder, just weight shift under the C/G, and it flies perfectly. As far as maximum velocity and time goes, a pilot named John Heiney has performed 50 full loops in his king post Hang Glider, reaching speeds in excess of 90 mph to do it.

This week is the anniversary of the Wright Brothers flights in their gliders, which I believe led to the king post hang gliders of today, the geometry is basically the same.

Just for fun, here is a video of some bowsprit king post Hang Gliders, using gravity, incline and penetration to attain velocity.

=========================================================================================================

This is not the easiest of calculations and depends greatly on experimental data. Here is a good link (pdf) by the American Institute of Aeronautics and Astronautics that has data and calculations for four hang gliders from the same manufacturer ( Wills Wing ) which will give you some idea of what is involved in answering your question.

If you are just interested in the terminal velocity going straight down, here are some results from this online calculator:

Mass: 240 lb

Cross-section area: 6 ft^2

Drag Coefficient: 0.3

Air density: 1.225 kg/m^3

Gravity: 1 g

Calculation results:

Terminal Velocity (metric)            102.0914 m/s (367.5290 km/h)

Terminal Velocity (imp)  334.9414 ft/s (228.3719 mph)

I hope this is of some help in answering your question. Welcome to our forum!

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I am never interested or scared of going "straight down". ha.  It is hard to push the stick forward when you are looking at the ground, but   It's absolutely necessary sometimes or the wing doesn't fly, or you die, in a hang glider it's opposite, you pull the control bar in, to gain penetration. Thank you for sending that link to me, it was the best I've seen.

I was born in 1946, right into an American Airlines DC-3 that my dad was flying, had my private license in Torrance Ca. during high school, where surfing and hang gliding were "invented" ha. Then moved to Telluride Co. in 1970, where High Mountain Hang Gliding was "invented", So I really was lucky and related to the file you sent.

I am sending a link, of John Heiney training video called "In and Out", that shows how to properly, "ground handle" a Hang Glider, in 20-25 mph. wind. The first part is what i'm talking about, and with music, outstanding.

Trying to figure out in my mind, how to create the same effect, using "fans of some kind,  off camera., pointed at a Hang Glider.  Maybe it would take too many fans to be practical, I don't know.  It would be worth a shot though.  it would make a good "trainer".

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Yes, I am sure you were not interested in going straight down. I was interested myself in what the terminal velocity would be in that case.

You are welcome for the link. It is interesting; I wish I had the time to go through it in detail.

I take it you are around 75 years old, and still hang gliding? You have my respect.

Although my main interest is marine engineering, I also do some flying whenever I have some time, in an aerobatic citabria. That provides more than enough flying adventure for me. I will leave the hang gliders for more daring enthusiasts like yourself.

For your training demo, there are some very large Industrial fans available, but you might be better off with a couple of large blower motors. Just a thought.

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I quit "daring" so much, awhile back, but I always put training first on the lists.  As far as Hang Gliding goes, I saw the transition into "para chute gliders", in the late 80's.  They came in droves, all across the country, and now, the air framed fliers and the parachutes floating around, wasn't much fun, and there were so many, sometimes.

That has been a conundrum for me, to see the performance numbers on a king post hang glider, that have been there since the late 70's, and the new numbers on these "para glider" wings, shocks me why anyone would choose a wing that you couldn't penetrate in a moment, or at all, sometimes, and then there is the "partial collapse" part of it in a "paraglider".   The two, "airframes" are so completely different, but somehow the ushpa marketing campaign included the "hanging" part of the word, so they considered themselves in the "Hang Glider" family, pretty crafty actually.

Nothing to be done about how many people are buying these Chinese made paragliders, and training how to fly them, (and there are allot of them),

but training a pilot to fly a "flex wing airframe", is harder to learn for sure, but easy to master.

That's the nature of today's recreational flying though, they just want to do it quickly, and be a paying member of a club.

Back to the "wind machine", for me it would be a way that new Hang Glider Pilots could "take a first ride" on this, have a video of their "static flight", with music, and at the same time feel the pure beauty of the craft above them. You have to learn ground handling sometime, why not learn it well, right off the bat.

But how to build this portable "wind machine" is still beyond my limited skills for now.

Your post to me about the 4 wills wing gliders that were tested, was the best.

I have been looking for the same comprehensive documentation for a "paraglider" wing, but nothing to match Mr. Dees' paper. There should be one though, so people could make an honest decision, especially be it that, "collapses" have taken so many lives in the PG   world, and quite a lot less in HG.

The risk reward part of it is high for PG, and for me again, being able to penetrate, is job one, something a paraglider can't do naturally.

Bottom line is training, training, training.

Boy, I'm a new guy and longwinded and off topic, but, "at least we have the wind".

That picture of your airplane upside down is awesome, I can tell that you are a "stick and rudder guy"? and love to fly.

Thanks again.

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