How can a glider or an airplane do a loop without thrust

Main Question or Discussion Point

I have to admit I am not good on physics but I am willing to try to understand how is possible for a plane or a glide that's falling without thrust applied downward to make a loop (by changing direction or using the elevators on the tail of plane, like in this picture.

I am try to write a program to simulate the motion of this object flying using this code (I consider only gravity for the moment not drag nor lift)
Code:
tempgy = g * frametime ; // acceleration of gy
tempay = ((thrust / m) * 32) * frametime * sin(degtorad(dir)) ; // acceleration of thrust y
tempax = ((thrust / m) * 32) * frametime * cos(degtorad(dir)) ; // acceleration of thrust x
y -= (vely + tempay/2 + tempgy/2) * frametime   ; // update position y
x += (velx + tempax /2)* frametime  ; // update position x
vely += tempgy + tempay; // update velocity y
velx += tempax; // update velocity x
but offcurse with this code I only consider the sin and cos of the thrust applied to glider, what you can suggest me to do ? What other force applied to the airplane that will make him loop by changing the angle of elevators ? Best regards

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Nidum
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Look up Kinetic Energy

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jbriggs444
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What other force applied to the airplane that will make him loop by changing the angle of elevators ?
That would be lift -- a force at right angles to the current line of motion.

If you consider only gravity and thrust and if you are modelling a glider (thrust = 0), the motion you simulate will always be that of a thrown rock. A parabola.

Which control surfaces are changing at the beginning of the loop? I can see the loop occur if a change in the tail sections elevator moves upward and occurs at a rate that prevents the plane from stalling. Is the plane's flaps involved as well to generate the loop?

Khashishi
Code:
tempgy = g * frametime ; // acceleration of gy
tempay = ((thrust / m) * 32) * frametime * sin(degtorad(dir)) ; // acceleration of thrust y
tempax = ((thrust / m) * 32) * frametime * cos(degtorad(dir)) ; // acceleration of thrust x
y -= (vely + tempay/2 + tempgy/2) * frametime   ; // update position y
x += (velx + tempax /2)* frametime  ; // update position x
vely += tempgy + tempay; // update velocity y
velx += tempax; // update velocity x
What you have is a reasonable simulation of a rock. For a plane, you need to keep track of the pitch angle as another state variable. Then you need to assign a lift which depends on the speed and angle of attack. And you need to include drag. Note that drag necessarily increases with lift. You can't gain elevation without sacrificing some speed.

CWatters
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A glider performing aerobatics trades Potential Energy and Kinetic Energy back and forth (with some energy lost to air resistance/drag).

What you have is a reasonable simulation of a rock. For a plane, you need to keep track of the pitch angle as another state variable. Then you need to assign a lift which depends on the speed and angle of attack. And you need to include drag. Note that drag necessarily increases with lift. You can't gain elevation without sacrificing some speed.
Yes flaps in case of airplane would be involved indeed, the code I put there is just one example it's not the full code but it simulate well a rock ; (dir) is the variable for the direction I could change, isn't enough for pitch angle ?

FactChecker
Gold Member
Aerodynamic force can be a lot greater than the thrust from any engine.

I looked up rose curves and polar equations for r^2 =a^2sin2theta. If the equation for that that curve was modified slightly and reflected on polar graph paper, that curve looks similar to your sketch. The line of the curve heading downward could represent the plane's angle of attack and possibly other information. I sometimes look for an existing equation whether it be in polar or rectangular to aid in modeling physical behavior. Hope this helps

jbriggs444
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2019 Award
Yes flaps in case of airplane would be involved indeed, the code I put there is just one example it's not the full code but it simulate well a rock ; (dir) is the variable for the direction I could change, isn't enough for pitch angle ?
I do not think you would be using flaps as control surfaces to initiate a loop. That's what the elevators are for.

I think the domain on theta needs to be limited after the reflection to [3pi/2,pi/2] or [0,pi] depending on how the graph is to be visualized. One quadrant is needed for the line entering the loop and the second quadrant representing the loop itself.

I was not saying the flaps would be used to initiate the loop but in synchrony with the elevator itself. I have used flaps and the elevator together on model aircraft for loops and it worked ok. The flaps seem to help smooth the curve until the plane is upside down and returning back towards earth and which point the flaps are level relative to the rear part of the wing. I was merely asking a question

Nidum
Gold Member
There is always scientific method to fall back on when all else fails . Perhaps a diagram showing the forces acting on the glider might clear a few things up ?

CWatters
Homework Helper
Gold Member
+1

It would be interesting to write equations (probably simplified) for each of the four forces plus a control input and then just "let it run". The control input will need to change with time.

Aside:I've flown aerobatics in both gliders and powered aircraft. You can forget complications like flaps.

Loop-the-Loop with a Flying Hoopster

Most paper airplanes are flat, but these paper hoops can really fly!

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https://www.scientificamerican.com/sciam/cache/file/9A8F3141-AEB1-4615-AE1DA6F30B4DE59D.jpg?w=590&h=393&FEC0D52A-E684-4E89-8BF2E6230BD056F0

Soar away sans wings! Try this activity to see how a simple paper craft can fly just as well as a traditional paper airplane. Credit: George Retseck
Key Concepts
Gravity
Thrust
Lift
Drag

Introduction
Paper airplanes are fun to make and fly. Most designs resemble miniature planes—made of folded paper, with wings, stabilizers and sometimes even flaps. These creations look like they are ready to soar. There are some designs, like the one you can try in this activity, however, that look so awkward one might imagine they would not fly at all. Find out if it will really soar!

Background
Although there are many different paper airplane designs, almost all of them have a flat winglike structure, which, like a traditional plane, helps create lift to keep the plane in the air. The plane in this activity, which is reminiscent of Phillip Swift's design entered in Scientific American's , gets the lift needed to glide from two rings, instead of wings. Normal wings have wing tips that generate vortices, adding drag (which isn't ideal for an object trying to stay aloft). The lift-providing rings have no wing tips and so they have less drag. The streamlined shape of the "hoopster" also makes it easy to throw accurately.

Materials

• Scissors
• Ruler
• Pen or pencil (optional, for measuring out paper to cut)
• 3-x-5-inch index card (or a file folder or some other stiff paper)
• Piece of printer paper (or similar stiff paper)
• Clear plastic tape
• Stiff plastic straw (that does no have a bendy top)
• Measuring tape (or long string)

Ok, my knowledge on physics and vector algebra is quite bad so I am just learning, be patient with me.
Based on this image

let's say my airplane have a direction of 15° and accelerating, then suddenly stop acceleration and point down nose of the plane, get some velocity and still without thrusting using the aileron make plane turn up again with the nose. With the formula I write before offcurse this movement will not be done because as soon I point down my nose on the plane and stop the thruster my plane will continue to fly down even if I change my variable (dir) because offcurse that's chained with the thrust part, so how can I could make chaning x and y if not thrusting with another direction controlled by tail aileron ?
Another question regarding the drag force, if my plane it's with thrust = 0 and I let it fall down it's creating velocity, so with drag added my plane tend to go backward (not considering air resistance or wind) what I'm doing wrong ?

jbriggs444
Homework Helper
2019 Award
let's say my airplane have a direction of 15° and accelerating, then suddenly stop acceleration and point down nose of the plane, get some velocity and still without thrusting using the aileron make plane turn up again with the nose. With the formula I write before offcurse this movement will not be done because as soon I point down my nose on the plane and stop the thruster my plane will continue to fly down even if I change my variable (dir) because offcurse that's chained with the thrust part
As you say, have a direction variable which models the plane's current pitch angle relative to the horizontal. You have vx and vy variables for the plane's current velocity. From these you can obtain the plane's current velocity angle relative to the horizontal. That would allow you to compute the pitch angle relative to the current velocity, aka "angle of attack".

Then you should proceed as @Khashishi has already suggested:

What you have is a reasonable simulation of a rock. For a plane, you need to keep track of the pitch angle as another state variable. Then you need to assign a lift which depends on the speed and angle of attack.
Another question regarding the drag force, if my plane it's with thrust = 0 and I let it fall down it's creating velocity, so with drag added my plane tend to go backward (not considering air resistance or wind) what I'm doing wrong ?
If your forward velocity is not adequate, gravity will indeed slow it down and cause it to move backwards. (e.g. a "hammerhead stall"). You need enough velocity going into the loop so that you still have forward velocity left over at the top of the loop.

So basically as my beautiful pic show

this is correct immagining the plane with initial v0 let it fall without thrust

jbriggs444
Homework Helper
2019 Award
So basically as my beautiful pic show

this is correct immagining the plane with initial v0 let it fall without thrust
What does that drawing depict?

An ideal airplane or paperplane, set in space and let it fall down freeely as stated before.

jbriggs444
Homework Helper
2019 Award
An ideal airplane or paperplane, set in space and let it fall down freeely as stated before.
No. What does it say? You show a plane moving both forward and downward and diagonally backward at the same time. Is that what you intend?

Sorry my drawing skill is very poor, the first plane is the step at time 0, my plane is on starting position with velocity 0 and thrust =0
The second plane is the action after 5 unit of time, my plane went backward and down because of the gravity and the drag as it get velocity but no thrust

by changing direction

This is achieved through aerodynamics such as the Bernoulli effect and the fact that air resistance is not identical against cross sections in the different axes.

FactChecker
Gold Member
Are you interested in simulating a reasonable path for a piloted glider, or in simulating all the physics that would give you a path?
The first is much easier than the second because there are a lot of flight paths that are possible for a piloted glider. You have a lot of freedom and just have to keep within certain limits.
Simulating the physics would get into more detailed aerodynamics and equations of motion.

jbriggs444