Question about speed of the flying body

[VioletHood]

I tried to find an answer everywhere but didn't found it and I am not strong at physics so please help me

I need to know equations for minimum speed required for some body to fly horizontally depending on it's mass , height of fligth and distance to fly . I mean object must travel some distance straight - without falling an inch - sustaining it's height during some given distance. As I understand subject - heavier bodies need higher speed to counter gravity to sustain their flight or they will simply fall or something like that. Is there any equations to find this speed if I know mass, height and distance?...object is bullet-shaped and all his dimensions is known. roughly mass is 800 000 kg , height is 5 m and distance is 100 m.

Can anybody help me with that?...

 

[davenn]

hi
welcome to PF

are you referring to something with or without wings ?

 

[VioletHood]

Hey! w/o wings. Body got shot from cannon. Body have no rocket propulsion as well. It's just body in form of a bullet on his own. :)

 

[davenn]

800,000 kgs is a huge object a decent sized ship

 

[VioletHood]

It's giant bullet ;) Any ideas for equations?

 

[russ_watters]

An object cannot fly horizontally without lift from wings or cotinuous thrust.

 

[Bandersnatch]

An object cannot fly horizontally without lift from wings or cotinuous thrust.

What if you had a spinning bullet with some angle of attack to its flight? That should generate some lift.

 

[VioletHood]

How bullets fly horizontally then? :O They are not declining up to some point...

 

[Bandersnatch]

How bullets fly horizontally then? :O They are not declining up to some point...

Why do you think they aren't?

 

[VioletHood]

Maybe you just got me wrong? Hm - object moves at some height.

 

[russ_watters]

What if you had a spinning bullet with some angle of attack to its flight? That should generate some lift.

Fair enough: or some lift generating mechanism like a lifting body or spin perpendicular to the direction of flight (for the bullet, the spin does not generate the lift, it just makes it stable -- the angle of attack may generate lift).

Generally, though, that doesn't happen for bullets.

 

[VioletHood]

Why do you think they aren't?

Because you can precisely hit a target with them.. I mean not declining drastically up to some point.

 

[russ_watters]

Maybe you just got me wrong? Hm - object moves at some height.

In general, bullets follow a ballistic path.

Because you can precisely hit a target with them.. I mean not declining drastically up to some point.

Incorrect: gun sights on bullets that travel any significant distance are adjusted to elevate the bullet's path.

 

[VioletHood]

Is there any equations for this?...

 

[russ_watters]

Yes. The concept is called "projectile motion" and this will explain in detail and provide the necessary equations for it:
http://en.wikipedia.org/wiki/Projectile_motion

 

[VioletHood]

This DO NOT consider MASS !

I need equation for projectile speed which will consider it's mass too as I say in OP.

 

[Bandersnatch]

Generally, though, that doesn't happen for bullets.

I'd rather say that it's not very significant here, not that it doesn't happen. Just a minor nitpick.

@VioletHood once in flight, and when air resistance can be neglected, the mass of the projectile doesn't matter. It's the same idea as with Galileo's observation that all objects fall at the same rate regardless of mass (again, disregarding air resistance).

If air resistance is to be included, which for low speeds and huge, compact mass as in the OP could very well be neglected, the equation of motion does include mass, but is also much more involved than the basic no-drag equation:
http://en.wikipedia.org/wiki/Trajec...rajectory_of_a_projectile_with_air_resistance

The above still disregards any lift generated by the angle of attack of the bullet, but again, that's not at all significant an effect unless you're talking about orbital velocities.

 

[russ_watters]

This DO NOT consider MASS !

I need equation for projectile speed which will consider it's mass too as I say in OP.

Mass is not relevant to the basic projectile motion equation because acceleration due to gravity is the same for all objects. The only impact mass might have for an object that doesn't generate lift is if drag is considered and the drag vs mass mix results in a different deceleration.

 

[VioletHood]

I'd rather say that it's not very significant here, not that it doesn't happen. Just a minor nitpick.

@VioletHood once in flight, and when air resistance can be neglected, the mass of the projectile doesn't matter. It's the same idea as with Galileo's observation that all objects fall at the same rate regardless of mass (again, disregarding air resistance).

If air resistance is to be included, which for low speeds and huge, compact mass as in the OP could very well be neglected, the equation of motion does include mass, but is also much more involved than the basic no-drag equation:
http://en.wikipedia.org/wiki/Trajec...rajectory_of_a_projectile_with_air_resistance

The above still disregards any lift generated by the angle of attack of the bullet, but again, that's not at all significant an effect unless you're talking about orbital velocities.

Too complex equation for me. xD Can you simplify it or it's impossible to fulfill my demand?

I always thought that make million ton projectile fly requires magnitudes bigger speed.

 

[russ_watters]

Too complex equation for me. xD Can you simplify it or it's impossible to fulfill my demand?

I always thought that make million ton projectile fly requires magnitudes bigger speed.

I'm sorry, but your question is based on a false premise, so it is not possible to fulfill your demand: you cannot make an object fly horizontal without lift (with speed alone).

 

[VioletHood]

I don't mean projectile should not fall at all. I allow him to lose some height - 10-20% during it's flight with distance of 100 m.

Ok if it's too complicated. I just want to know speed of my projectile to flew 100 mters and consider it's mass too.

 

[russ_watters]

I don't mean projectile should not fall at all. I allow him to lose some height - 10-20% during it's flight with distance of 100 m.

Ok if it's too complicated. I just want to know speed of my projectile to flew 100 mters and consider it's mass too.

OK, well that you can easily find using the projectile motion equations. Pick an exact fall distance, then give a try at using the equations provided to figure it out. Let us know if you get stuck.

 

[VioletHood]

russ watters and other guys who tried to help me, sorry - I am too noob for this and currently waiting for simple ready solution by much more competent people. :)

One person perfectly rephrased what I wanted to find out and this should change case.

Well the task consists in, that a body weighing 750 000 kg. started horizontally with some speed with height of 3 meters and after 100 meters of flight didn't fall lower then 2.5 meters. Question: "What speed is necessary for this person?"

Can someone help me now?

 

[russ_watters]

russ watters and other guys who tried to help me, sorry - I am too noob for this and currently waiting for simple ready solution by much more competent people. :)

Sorry, but that isn't how we do things here. This forum is for learning, not for getting other people to do the work for you. So please make an effort to learn from the information already provided. As I said, we'll help you if you get stuck.

 

[VioletHood]

Though mass is irrevelant for my question right? Problem is to make heavy body move at some speed and it will behave totally similar to lighter body in that case as I understood from another forum.

 

[A.T.]

a body weighing 750 000 kg. started horizontally with some speed with height of 3 meters and after 100 meters of flight didn't fall lower then 2.5 meters

If the speed doesn't drop, this is what you are looking for:
http://en.wikipedia.org/wiki/Lift-to-drag_ratio#Glide_ratio

If it's really just 3m above ground, this might also play a role:
http://en.wikipedia.org/wiki/Ground_effect_(aerodynamics)

 

[jbriggs444]

Though mass is irrevelant for my question right? Problem is to make heavy body move at some speed and it will behave totally similar to lighter body in that case as I understood from another forum.

Yes. As long as we can neglect air resistance, mass is irrelevant.

Now on to the task at hand...

Well the task consists in, that a body weighing 750 000 kg. started horizontally with some speed with height of 3 meters and after 100 meters of flight didn't fall lower then 2.5 meters. Question: "What speed is necessary for this person

The height of the start is irrelevant. Whether the body starts at 9.5 meters and drops to 9, starts at 3 meters and drops to 2.5 or starts at 0.5 and drops to zero, the important thing is the distance fallen.

So simplify and just think about a drop of 0.5 meters.

In the absence of air resistance, the horizontal velocity is irrelevant to how long it takes to fall 0.5 meters. That may be hard to swallow, but it is a truth about classical mechanics. For example, a man falling off of his 0.5 meter high seat on a bullet train takes the same amount of time to hit the floor as a man falling off his chair at the dinner table at home.

So simplify and compute the fall time for a drop of 0.5 meters. You can use the equation of motion for an object accelerating from rest at a constant acceleration: d = 1/2 a t² where d is the distance covered, a is the acceleration and t is time.

Now you know how much time you have. You already know how much horizontal distance you have to cover. It should be easy to compute the required speed.

Now... suppose that instead of a horizontal launch you aimed a bit high so that the object rose to a maximum of 0.5 meters above the horizontal path and arrived 100 meters away at the same height that it started. Could you get away with a lower launch speed in this case? How much lower?

 

[russ_watters]

If the speed doesn't drop, this is what you are looking for:
http://en.wikipedia.org/wiki/Lift-to-drag_ratio#Glide_ratio

If it's really just 3m above ground, this might also play a role:
http://en.wikipedia.org/wiki/Ground_effect_(aerodynamics)

No, this was specified to be a projectile motion problem.

 

[VioletHood]

Yes. As long as we can neglect air resistance, mass is irrelevant.

Now on to the task at hand...

The height of the start is irrelevant. Whether the body starts at 9.5 meters and drops to 9, starts at 3 meters and drops to 2.5 or starts at 0.5 and drops to zero, the important thing is the distance fallen.

So simplify and just think about a drop of 0.5 meters.

In the absence of air resistance, the horizontal velocity is irrelevant to how long it takes to fall 0.5 meters. That may be hard to swallow, but it is a truth about classical mechanics. For example, a man falling off of his 0.5 meter high seat on a bullet train takes the same amount of time to hit the floor as a man falling off his chair at the dinner table at home.

So simplify and compute the fall time for a drop of 0.5 meters. You can use the equation of motion for an object accelerating from rest at a constant acceleration: d = 1/2 a t² where d is the distance covered, a is the acceleration and t is time.

Now you know how much time you have. You already know how much horizontal distance you have to cover. It should be easy to compute the required speed.

Now... suppose that instead of a horizontal launch you aimed a bit high so that the object rose to a maximum of 0.5 meters above the horizontal path and arrived 100 meters away at the same height that it started. Could you get away with a lower launch speed in this case? How much lower?

Thanks! It's simple and useful explanation. This will help me for sure. ;)

 

[VioletHood]

If the speed doesn't drop, this is what you are looking for:
http://en.wikipedia.org/wiki/Lift-to-drag_ratio#Glide_ratio

If it's really just 3m above ground, this might also play a role:
http://en.wikipedia.org/wiki/Ground_effect_(aerodynamics)

Not sure about it. :)