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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Satellites

Two Reasons Why the Humanity Star is Not a Complete Waste of Time

If you have not seen this, you should look at this web page that describes The Humanity Star.  It is basically a nearly spherical object that was launched into space in January of 2018.  It has 65 reflective surfaces that will reflect sunlight while it is in orbit. The general idea is that whenever it is in the sun, it will be so bright in the sky that you can see it.

Normal satellites can be seen in orbit around the Earth from the ground.  What happens is that when it is dark on the ground, but still light at orbital altitudes (around 250 miles high and above), sunlight can reflect off the satellite and it can look like a star in the sky.  This happens just after sunset or just before sunrise.  If you are very patient and look up at the sky during these times (preferably from an outdoor hot tub), you can sometimes see objects that look like stars that are moving from south to north or north to south. To give you an idea, it should take them about 10 minutes to go from horizon to horizon.

The Humanity Star is so bright that it should be be visible during the day.  The web page talks about how this will be a beacon to draw humanity back together and to make them look to the stars.  I personally don’t think that a tiny star-like object in the sky will bring humanity back together unless the star-like object is getting bigger and bigger every day and has the potential to wipe out humanity.  Other people that I have talked to have a similar feeling, and so it seems like The Humanity Star really has no real value. Except it does. There are a few good reasons, some intended, and others maybe not.

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The Humanity Star. It is not in orbit in this picture. It is sitting on the ground. (From the website).

The true purpose of The Humanity Star was really to test the Electron rocket by Rocket Lab. This was the first flight of the Electron.  While Space-X just launched the Falcon Heavy, Rocket Lab launched a small rocket that can take only 150-225 kilograms to orbit for an estimated price of $5M.  This is a huge deal because constellation missions would like to spread out satellites.  It is incredibly difficult to truly distribute a constellation of satellites from a single launch vehicle (rocket).  If you could buy 8 tiny rockets that could take one or two satellites to orbit for the price of one medium sized rocket that could take 8 satellites, it would allow you to distribute the satellites immediately.

When you test a rocket for the first time, the probability of failure is quite high (like, explosively high).  Some companies give a special deal to satellite companies to launch their satellite on a very risky rocket launch. If it blows up, then everyone loses, but they are not out a huge amount of money.  If it doesn’t blow up, everyone wins – the rocket is proven to work, and the satellite gets to orbit for cheap. Other companies just launch dummy payloads in order to prove that the rocket works.  If it works, then they have a proven rocket.  If it doesn’t, no one is harmed.  This path doesn’t make the company any money (if the rocket works), but also doesn’t make people really angry (if it doesn’t work).

The Humanity Star was a dummy payload for the first test launch of the Electron rocket.  This is similar to Space-X launching a Tesla on the Falcon Heavy (another dummy load with an actual dummy in the driver’s seat). Instead of just saying that it was a test load, Rocket Lab made a big deal about The Humanity Star instead of talking about their super cool and super small rocket.

The second interesting thing about The Humanity Star is that it can actually be used to do science, even though it has no power or sensors or anything. The Air Force has many dummy spheres like this in orbit. The reason for this is that all objects in low Earth orbit feel atmospheric drag.  Since the projected area of a nearly spherical object is known exactly and basically never changes (since it looks exactly the same from every angle) the only change in the drag force that the object feels is due to changes in the atmospheric density. Normal satellites are strange shapes and have lots of protrusions, like antennas and such.  If the orientation of the satellite changes, the drag changes. It is often extremely difficult to model this behavior accurately.  So, simple spheres are used and are tracked with radars from the ground.

The Humanity Star will allow us to more accurately track the thermospheric density since it is really big (about 1 meter across) and pretty light (about 8 kg).  Its area to mass ratio means that the drag that it feels will be pretty big, so it will reenter the atmosphere pretty quickly (less than a year). Because it feels such a large drag, the drag force will be easy to determine and any changes will be caused by only by changes in the thermospheric density.  This is the type of research that I do!

Another really minor thing about The Humanity Star is that because it can be visible from just before sunrise to just after sunset, including the whole day, it could be used for educational purposes.  You see, a satellite’s orbit can be determined just by tracking how it moves across the sky.  If you point a telescope at the satellite in the sky and mark down the direction that the telescope is pointed, and do this over and over again as the satellite moves across the sky, the math is relatively easy to do to determine the orbit (well, students do this in Junior-level Aerospace Engineering classes). This is a great real life example that students could use to put their education to use! In the daylight!

Hopefully this has convinced you that The Humanity Star is not a complete waste of time and money!