# Question about speed of the flying body

1. May 9, 2015

### VioletHood

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?...

2. May 9, 2015

### davenn

hi
welcome to PF

are you referring to something with or without wings ?

3. May 9, 2015

### 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. :)

4. May 9, 2015

### davenn

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

5. May 9, 2015

### VioletHood

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

6. May 9, 2015

### Staff: Mentor

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

7. May 9, 2015

### Bandersnatch

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

8. May 9, 2015

### VioletHood

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

9. May 9, 2015

### Bandersnatch

Why do you think they aren't?

10. May 9, 2015

### VioletHood

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

11. May 9, 2015

### Staff: Mentor

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.

12. May 9, 2015

### VioletHood

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

13. May 9, 2015

### Staff: Mentor

In general, bullets follow a ballistic path.
Incorrect: gun sights on bullets that travel any significant distance are adjusted to elevate the bullet's path.

14. May 9, 2015

### VioletHood

Is there any equations for this?...

15. May 9, 2015

### Staff: Mentor

16. May 9, 2015

### VioletHood

This DO NOT consider MASS !

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

17. May 9, 2015

### Bandersnatch

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.

18. May 9, 2015

### Staff: Mentor

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.

19. May 9, 2015

### VioletHood

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.

20. May 9, 2015

### Staff: Mentor

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).