Starship is performing maneuvers that have never yet been attempted. It is a 9 m wide, 50 m tall rocket that falls out of the sky horizontally, before flipping and landing vertically.
The landing attempts so far have raised a lot of questions:
- Why are they doing the belly flop?
- Why are they doing the flip maneuver so close to the ground?
- Will this ever be safe enough for humans?
- Why don’t they just start the flip maneuver earlier and ensure there’s enough time to make corrections if something goes wrong?
- Are the experienced G forces reasonable?
- Should SpaceX just switch to a Falcon 9 first stage style of landing?
This article will address the different aspects that affects Starship’s landing maneuver:
- Different options of engine combinations at the point of landing
- Terminal velocity
- Gravity Drag
- Thrust-to-weight ratio
- Engine Throttling
Starship’s Transition from Belly Flop to Tail Down
The Starship landing maneuver is a new and unique style of landing a rocket. Starship begins by falling out of the sky, belly first, to expel the greatest amount of velocity as physically possible while in freefall. At around 500 m (1640 ft) in altitude, it will light two Raptor engines, gimbal them full tilt, fold in the rear flaps, and swing from horizontal to vertical so it can land tail down on its landing legs.
When the rear fins retract and tuck in, the nose portion experiences a substantially higher amount of drag compared to the tail section. This combined with the firing Raptor engines cause the tail section to rotate under the nose, making the rocket vertical. Sometime in the future, SpaceX might add hot gas thrusters to farther aid in the rotation.
As a result of Starship igniting the Raptor engines horizontally, the engines must receive the propellent from special tanks called header tanks. The reason behind this is because the engines cannot take in any air. If they continued to take liquid methane (CH4) and liquid oxygen (LOX) from the main tanks, the engines would end up ingesting air, which could result in a RUD (Rapid Unscheduled Disassembly) of the engines.
Propellant Settling on Starship’s Belly
Due to the horizontal orientation of the rocket, the propellants settle on the belly or windward side of Starship. This is because the rocket is being slowed down by the ever thickening atmosphere, which pushes the propellant down on the belly.
Since the feed lines from the tanks to the Raptor engines are located on the bottom of the rocket, during the belly flop, the engines would receive mostly air if they tried to pull propellant from the main tanks. These header tanks are located in the nose portion and in-between the two main tanks of Starship, they remain nearly full until landing maneuver. The drain valves on the header tanks are positioned at a slight angle to aid in the maneuver.
Lighting the engines at a horizontal orientation produces a significant amount of horizontal velocity, which will then lead to the rocket intentionally over rotate to cancel out the injected horizontal velocity.
Terminal Velocity during a Rocket Landing
One purpose of the belly flop maneuver is to scrub off and reduce as much velocity as possible passively. The other purpose is to control the peak temperature and orientation of Starship during orbital reentry. As a general rule, the lower the rocket’s terminal velocity is, the later it has to perform its landing burn, because the engines don’t need to burn off as much velocity anymore.
Starship’s Terminal Velocity
The definition of terminal velocity is: the maximum velocity an object reaches as it falls through a fluid, such as air, or when the downward force or gravity equals the force of drag. Terminal velocity changes as the conditions around the object change. When air pressure increases and the atmosphere gets thicker, terminal velocity gets slower, because an object experiences more drag.
Starship’s maneuver can be compared to that of a skydiver during freefall. When a skydiver falls belly first they have the most drag on their body as possible, which means their terminal velocity is at a minimum. If they were to flip to their feet or head first, there would be much less surface area for the air to push against the sky diver.
Similarly, Starship has the ability to change its orientation and therefore terminal velocity based on how for the flaps are extended outwards. The flaps in this case resemble the arms and legs of a skydiver. If the flaps are more extended, the drag on the vehicle will increase and if they are folded in, the drag will decrease, thus making the terminal velocity faster. Through this, a clear difference is shown between the descent of the Falcon 9 first stage and Starship. Falcon 9 has a much higher velocity than Starship as it descends through the atmosphere, because there is less surface area to increase the drag (engines first).
Comparing Falcon 9 to Starship
Declan Murphy from flightclub.io calculates highly accurate simulations of rocket launches and, in this case, SpaceX descent profiles. Flight Club has the ability to compare SN8’s flight profile to Falcon 9’s NROL-108 mission. The simulation shows that SN8 was falling at a maximum velocity of 150 m/s (about 490 f/s) and then, because of the ever thickening atmosphere, slowed to just 90 m/s (about 250 f/s), its peak velocity would be higher. but its velocity just before the flip maneuver would still be slow enough to perform a safe landing.
On the other hand, the Falcon 9 comes in for landing much faster. Even though its peak velocity is higher, because it starts its descent at a much higher altitude, the Falcon 9 will still reignite its engine(s) while its terminal velocity is at 310 m/s (about 1020 f/s). Compared to Starship, Falcon 9 has a higher velocity, because it has less of a surface area to induce drag. Similarly, a pencil will fall faster than a piece of paper, because the pencil has far less surface area to increase drag than a piece of paper.
Despite the difference of 220 m/s (about 720 f/s) being only a fraction of orbital velocity, which is 7,800 m/s (about 17,500 mph), the belly flop maneuver might not seem to have a big enough effect. However, when observing the elements of thrust to weight ratios and how much propellant is required for various thrust to weight ratios, every meter per second counts.
Thrust to Weight Ratios
In order for a rocket to hover, it has to produce the same amount of thrust that it weighs, assuming there is no atmosphere. An object with a mass of 1 kg (2.2 lbs) weighs 9.8 newtons on Earth. This is because Earth’s gravity pulls at a force of 9.8 N. In this example, a rocket weighs 1,000 N (or 1 kN) and produces 1,000 N of thrust in the opposite direction, meaning that the thrust-to-weight ratio will be 1:1. The net acceleration of this vehicle in this case will be zero, because the thrust of the rocket is exactly counteracting Earth’s pull on it.
When a rocket produces 900 N of thrust while weighing 1000 N, the thrust to weight ratio drops to 0.9:1. Every second that the rocket has this thrust to weight ratio, it will increase its velocity and accelerate downwards. However, if the rocket returned to the thrust to weight ratio of 1:1, it would not hover, but instead constantly descend at its current velocity. A thrust to weight ratio of 1:1 simply means that the rocket’s current velocity is not changing, whether it is hovering or moving.
Returning to a Hover
In order to return to a hover, the rocket must increase its thrust to weight ratio to above 1:1 to cancel the downward velocity. In this example, the rocket would increase its thrust to 1,100 N and once it reaches zero velocity, it returns to 1,000 N of thrust.
The opposite direction is also applicable. Assuming there is no atmosphere, if a hovering rocket increases its thrust to weight ratio to 1.5:1, it would accelerate upwards. To return to a hover, the rocket must produce a thrust to weight ratio under 1:1 until its velocity is zero again, where it can return to a thrust to weight ratio of 1:1 to sustain zero velocity.
Throttling on Landing
Thrust to weight ratios are a major factor when throttling an engine for landing. Using the Falcon 9 as an example, it has too much thrust on just one engine at its minimum throttle setting to hover. In order for the Falcon 9 to land nominally, it will start its landing burn at 70 percent throttle, so it can adjust for coming in too fast or too slow. Using on board computers and various other instruments, the Falcon 9 will aim to have zero velocity right as it arrives at zero meters in altitude, performing its hoverslam.
Braking with a Car
In this example shown in the graphics below, the stop sign is the ground and the car is the falling rocket. A car is travelling at 50 km/h (31 mph) as it approaches the stop sign. The goal is to stop the car right at the stop sign without ever touching the accelerator or letting off the brakes.
Applying the brake at full force would be equivalent to a rocket relighting its engines at a 100% throttle setting, while not applying force to the brakes is the minimum throttle setting. Applying force to the accelerator would be the same as not relighting the engine at all.
Letting off of the accelerator is like lighting a rocket’s engine, due to the engine braking in internal combustion cars, or the regenerative braking of hybrid and electric vehicles. Teslas have the ability to choose the amount of regenerative braking, which is similar to different throttle settings of a rocket engine.
Throttling with a Car
A low amount of regenerative breaking would equal a minimum throttle setting, while a high amount of regenerative braking would equal a high throttle setting. A low setting would result in releasing the accelerator earlier, while a high setting would result in releasing the accelerator later, because the car would slow down faster.
Applying different amounts of force to the brakes is similar to throttling a rocket engine. If a car begins braking early, then it can apply less pressure to the brakes to make the car get closer to the stop sign. However, if a car stops short of the stop sign after letting off the brakes entirely, it is the same as a rocket reaching zero velocity above the ground and falling the rest of the way.
With an understanding of thrust to weight ratios and how to throttle and engine on landing, it is easier to learn how gravity loss determines the optimal thrust to weight ratio to maximize the use of the remaining propellant.
Gravity Loss during Landing
Gravity loss is when a rocket is using an engine to fight gravity. In this example, a rocket starts with a thrust to weight ratio of 1:1. Every second the engine produces the same amount of thrust as the rocket weighs, it is simply wasting propellant without accelerating.
In order to slow down a rocket, the thrust to weight ratio needs to be higher than 1:1. With a thrust to weight ratio of 1.1:1, 91% of the rocket’s currently used propellant is fighting gravity, while the other 9% are used to get the rocket to where it needs to go.
With a thrust to weight ratio of 1.5:1, 2/3rds of the propellant is used fighting gravity while 1/3rd of the propellant is used accelerating the vehicle. By doing this, the rocket has increased its thrust by 36% compared to a thrust to weight ratio of 1.1:1, which is five times the net acceleration. A thrust to weight ratio of 1.1:1 would result in a net acceleration of 0.1 G, whereas a thrust to weight ratio of 1.5:1 would result in a net acceleration of 0.5 G.
Going Higher and Higher
Increasing the thrust to weight ratio to 2:1 uses 50% of the propellant for fighting gravity and the other 50% for accelerating the vehicle. In this case, the thrust is only increased by 33%, but the rocket produced twice the amount of acceleration compared to a thrust to weight ratio of 1.5:1.
With a thrust to weight ratio of 3:1, only 1/3rd of the propellant is used fighting gravity, while the other 2/3rds are used to accelerate the vehicle. The thrust was increased by 50%, while the rocket doubled its acceleration. There will always be propellant lost to fighting gravity unless there is no gravity.
Using the Falcon 9 and its landing burn as an example, it would, with a low thrust to weight ratio of only 1.1:1, have to start its landing burn at a higher altitude, as it is only decelerating at a net acceleration of 0.1 G. This would result in wasting a lot of propellant as the engines would have to run for significantly longer.
If Falcon 9’s thrust to weight ratio in this example would be 2:1, it would have a net acceleration of 1 G, it could start its landing burn way closer to the ground and would waste less propellant as the engine would not run as long.
Starship Flipping at Different Altitudes
The first reason Starship flips so close to the ground is to decrease the terminal velocity as much as possible. This would therefore decrease the amount of deceleration work that the engines have to do to bring Starship to a soft landing.
Each of the three Raptor engines installed on the bottom of Starship inside the skirt can throttle between 40% and 100% of maximum throttle. This allows for different thrust combinations by throttling the engines to different percentages. A single engine can produce between 880 kN and 2,200 kN of thrust, with two engines this goes up to 1760 kN to 4,400 kN of thrust, and with all three engines running, the thrust goes up to between 2,640 kN to 6,600 kN.
For the flip maneuver, different engines and failsafe combinations are possible to have the same outcome. If three engines are running at their minimum throttle of 40%, the thrust-to-weight ratio would be around 2:1. This is more than one Raptor at full thrust and would result in starting the landing burn very late, as to not cause the rocket to start going up as the vertical velocity is cancelled out.
If Starship was to lose one of the three engines, the two remaining engines could throttle up to match the thrust output of all three. In the scenario of only lighting one engine, the landing burn could be started much earlier, however, the max thrust-to-weight ratio achieved would only be 1.6:1. Doing so would require substantially more propellant compared to lighting all three engines, or even two. From a contingency point of view, if the one engine running was to fail, there would not be enough time to relight another one.
Different Flip Altitude Options
Starship has various different options for the starting altitude of the flip maneuver. The earliest that it can perform the flip maneuver is at 2.5 km (1.5 miles) in altitude with two engines during the flip, then shutting one off, and keeping the other at nearly a minimum throttle setting.
The lowest Starship can begin the flip maneuver is 300 m (980 ft), which requires all three Raptor engines at the highest throttle setting. Starship and its occupants would experience 4.5 G’s during the landing maneuver at this altitude.
Starship can also flip anywhere between 2.5 km and 300 m. At 550 m (1800 ft), Starship has the ability to shut down different numbers of engines, while not having a long and inefficient landing burn.
A high altitude flip at 2.5 km (1.5 miles) would require 370 m/s (1200 f/s) more delta-v (change in velocity) than starting at 550 m (1800 ft). Since it takes approximately 7,800 m/s (17,500 mph) to orbit, using 370 m/s (1200 f/s) to land will take away from the payload capacity. Doing the flip maneuver 2 km higher could mean putting 20 t less payload mass into orbit. This is because the 370 m/s required for landing would not be used to put the payload in the orbit.
The Crew during the Flip Maneuver
As SpaceX’s eventual plans are to send people to Mars, the landing maneuver necessary to do this task has yet to succeed. Currently, the Raptor engine is still in its early stages of development and has much more testing to go through. As the reliability of the engine increases, so will the reliability of the landing maneuver. Starship will have to successfully complete a multitude of tests before humans will ever fly on it.
Experienced G Forces
The peak G force during the flip maneuver is only 2.5 G’s, or 2.5 times the force of Earth’s gravity. Passengers might feel some disorientation during the flip from horizontal to vertical, but the stress on their body will not be higher than what they would experience on most roller coasters. SpaceX might install rotating seats in the future to help keep the G forces experienced on the body in only one direction.
In fact, the nose of Starship doesn’t move an incredible amount, despite the tail whipping from horizontal to vertical aggressively. Compared to Starship, a Flacon 9 can reach five G’s during its landing burn.
Starship is performing a new and unique landing maneuver. No other rocket or company has attempted such a complex method of rocket recovery ever. The affects and aspects of terminal velocity, gravity drag, and gravity loss are considered to find the optimal flip altitude, in order to compromise efficiency and safety.
SpaceX concluded that the optimal altitude to begin Starship’s flip maneuver is around 550 m. At this altitude, Starship uses that most efficient amount of delta-v at around 250 m/s, while also having capabilities to land safely in the event of an engine malfunction. It will allow Starship to ignite its engines and use an optimal thrust to weight ratio of 1.6:1 to decelerate and land.
The mass of the payload that Starship can put into orbit can also be determined by the altitude at which it performs the flip maneuver. The less delta-v used on landing means more delta-v can be used to place objects and/or humans into orbit. After all, SpaceX’s overall goal is to use Starship to eventually fly humans to the Moon, Mars, and beyond.