Rockets

Max-Q and Why Does it Matter?

In a rocket launch, they almost always talk about Max-Q, which is the point in the launch sequence where the rocket experiences the maximum dynamic pressure. First, let’s talk about what that actually means.

The rocket, as it is going up into space is experiencing three forces: gravity (down), thrust (up), and atmospheric drag (down).  Gravity is probably obvious, since you are probably sitting in a chair or on the couch and are feeling its effects (well, you are probably feeling the normal force from the chair that is pushing up on your backside, but let’s just say that you are feeling gravity). Thrust is what the rocket does as it expels fuel to make it go up. I have a post on that.

I also have a post on drag and terminal velocity if you would like a refresher on what all of that means. But, as a tiny backstory, atmospheric drag is like friction that an object feels as it moves through a fluid. So, when you are riding a bike, you feel drag, which makes it so you have to pedal harder into a headwind than a tailwind. This force is proportional to the density of the medium (it is MUCH harder to ride a bike underwater than it is in the atmosphere!), and the velocity squared (when you go twice as fast, you have to pedal four times as hard).

Returning to the subject at hand:

When the countdown ends and the rocket starts to fire, but before it starts to move, there are two forces acting on the rocket: gravity and thrust.  Thrust has to be a bit bigger than gravity for the rocket to start moving, otherwise the rocket will just sit there.  When the rocket starts moving upwards, it gain speed, and starts to experience a drag force.

Now, if the rocket flew horizontally, or if the atmosphere extended upwards forever, the drag force would increase and increase and increase as the rocket got faster and faster and faster.  As it happens in reality, the rocket launches mostly in a vertical state, and the atmospheric density decreases quite rapidly with altitude.  By about 23 km altitude, the atmosphere has decreased down to about 10% of its density.  For reference, airplanes fly at about 1/2 of this altitude, so the density is about 33% of its sea-level value.

The situation with the rocket, then, is that it starts to accelerate and the drag force starts to grow dramatically, since the force is related to velocity squared:  whenever the speed doubles, the force quadruples.  But, at the same time, the density is decreasing, so the force is weakening because of this.  At some altitude, the decreasing density wins out over the increasing velocity, and the drag force starts to decrease.

It is this point – where the increasing velocity is balanced by the decreasing density of the atmosphere and the drag force starts to decrease that is called Max-Q.

Screen Shot 2018-06-24 at 4.27.21 PM
A plot of the drag on the rocket as a function of altitude (in meters). The drag force is negative at this stage, since it is towards the ground.  Max-Q happens around 11 km in altitude in this simulation.

Now the question is – why do people care?

Well, rockets are really unstable. The thrust is coming out the back end and they are extremely long and narrow.  The thrust vector has to be right through the center of mass of the rocket in order for it to not rotate.  If the thrust vector is off, it could easily start to roll over.  If thrust and gravity were the only forces, it would be a bit complicated to control, but when you add in aerodynamic forces, it becomes even more complicated.  Older rockets (and model rockets!) used to have fins in order to help with this.  The fins made it so that if the rocket tipped at all, the aerodynamic forces on the fins would help correct for the tipping and apply a restorative force back into a non-tipping orientation. See the picture below.  There are aerodynamic forces all along the rocket, but the fins have the largest forces, so those forces win, and the rocket will rotate around the center of gravity and restore back to vertical.  With no fins, this restorative force doesn’t exist, since the forces along the rocket are all roughly equal, which makes it so that the rocket may or may not rotate one way or the other around the center of gravity.  Because of this, the rocket motors have to solve the issue all on their own.

Slide1

So, the drag force makes is a bit harder to control the rocket. Most rockets use computers to figure out how the rocket is tilting and adjust the thrust vector of the engine to rotate the rocket back to vertical.

If the computer stopped working and the rocket couldn’t adjust back to vertical, what would the problem be? The problem is that the rockets are not exactly super rigid and made out of super-strong materials, since they are designed to be as lightweight as possible.  It is designed to fly like an upright pencil through the atmosphere.  If you were to turn the pencil over and try to shove the pencil in a sideways configuration through the atmosphere, the rocket would probably shred to bits.  This is very bad.  So, the rocket needs to be aimed upwards as much as possible.  Any deviation from this upright position, and the aerodynamic forces could rip the rocket apart.

Slide2
If the rocket tilts too far, the forces on both sides of the center of gravity with cause the rocket to break apart. That is not good.

Max-Q is the time during the rocket’s flight in which the aerodynamic (drag) forces are the strongest.  So, you really don’t want the rocket to tip or do anything wonky during this time.  After Max-Q, the force decreases quickly, and the engineers can relax a bit.

It is around Max-Q, where the rocket starts to tilt a bit and rotate towards the horizontal direction.  This is because rockets only go upwards to get to their correct altitude.  They really need to go horizontally at about 7.6 km/s (that is fast).  If the rocket were to go straight up to like 500 km, then tilt over, it wouldn’t work very well, since it takes a long time to accelerate up to 7.6 km/s. Turning down low allows the rocket to take a while to get up to 500 km and take a while to get up to 7.6 km/s speed.  The rocket times it just right so that both are met at about the same time.  The location of Max-Q is where this tilting starts.

 

 

 

 

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