Lunar Lander Fuel Calculation Formula: Stopping Precision

how much fuel to stop a lunar lander formula

The Apollo 11 mission almost ended in disaster when a fuel light blinked on as the lunar module was on its final descent to the moon's surface. The astronauts, Buzz Aldrin and Neil Armstrong, had to make it to the lunar surface in 60 seconds or less. They had only 15 seconds of fuel left when the lander touched down. The amount of fuel required for a lunar landing depends on several factors, including the lander's weight, the presence or absence of an atmosphere, and the desired descent speed. In general, landing requires more energy than ascent.

shunfuel

Lunar landers require more fuel to land than to take off

Firstly, let's consider the change in weight due to fuel consumption. During landing, the lunar lander is full of fuel, whereas during takeoff, it is almost empty. This change in mass affects the delta-V costs of the maneuvers, with the landing phase requiring more fuel to achieve the same delta-V as the takeoff phase.

Additionally, the descent phase of a lunar landing is typically slower than free fall, which increases the fuel requirement. To achieve a controlled descent and ensure a safe landing, more fuel is needed to counteract the pull of gravity and slow down the lander.

Furthermore, the Moon's lack of atmosphere also contributes to the increased fuel requirement during landing. On Earth, spacecraft can use the atmosphere to help slow down during descent. However, on the Moon, there is no atmosphere to provide this assistance, requiring more fuel to be burned to slow the lander's velocity.

The specific fuel requirements for lunar landers vary depending on the mission and the spacecraft design. For example, the Apollo 11 lunar module consumed just over 2200 kg of fuel to return to lunar orbit, while the HLS Starship lunar lander requires multiple engine burns and propellant to reach the lunar surface and return to orbit.

In conclusion, lunar landers require more fuel to land than to take off due to factors such as fuel consumption affecting weight, the need for a controlled descent, and the absence of an atmosphere. These factors collectively contribute to the increased fuel requirements during the landing phase of a lunar mission.

shunfuel

The Apollo 11 lunar module nearly ran out of fuel during descent

The Apollo Lunar Module (LM) was the first crewed spacecraft to operate exclusively in space and remains the only crewed vehicle to land beyond Earth. The Apollo 11 LM, Eagle, was guided by a computer that, at 3:08 pm U.S. Eastern Daylight Time (EDT) on 20 July 1969, opened valves in its descent propulsion system, causing nitrogen tetroxide oxidizer and aerozine 50 fuel to come into contact and ignite. The descent engine fired for a little over 12 minutes, bringing Eagle and its crew from a 54-by-66-nautical-mile lunar orbit to an elliptical orbit with an apoapsis 50,000 feet above the Moon's Earth-facing Nearside hemisphere.

During the final approach, the vehicle pitched over to a near-vertical position, allowing the crew to see the lunar surface for the first time. At this point, manual control was enabled for the commander, who had enough propellant to hover for up to two minutes to survey the landing site. However, the computer was steering Eagle toward West Crater, a boulder-strewn impact crater the size of an American football field. Commander Neil Armstrong assumed manual control early, levelling Eagle's descent and scooting the LM almost horizontally across the lunar sky.

The landing was softer than anticipated, and the LM's landing legs had enough suspension to absorb the impact. The LM's development was plagued with problems, and the landing could have been aborted at almost any time by jettisoning the descent stage and firing the ascent engine to climb back into orbit. If flight controllers on Earth had estimated a slimmer propellant margin, they may have called on Armstrong to abort the landing, as per mission rules.

shunfuel

The delta-V cost of landing is higher than that of taking off

The delta-V cost of landing is indeed higher than that of taking off. Delta-v, or delta-velocity, is a scalar quantity that measures the impulse per unit of spacecraft mass required to perform a manoeuvre, such as launching or landing. It is dependent on the desired trajectory and not on the mass of the space vehicle. This means that while more fuel is needed to transfer a heavier satellite from low Earth orbit to geosynchronous orbit, the delta-v required is the same.

Delta-v is also additive, which means that rocket burn time has a greater effect later in the mission when more fuel has been used. This is important when considering the delta-v budget, which is the estimate of the total change in velocity required for a space mission. The delta-v budget is used to determine how much propellant is required for a vehicle of a given empty mass and propulsion system.

The delta-V cost of landing a spacecraft is higher than that of taking off because landing requires more energy than ascent. This is due to several factors, including the need for a de-orbit manoeuvre, ballistic coasting, braking, and the gravity turn during the braking manoeuvre. Additionally, there are usually more steps involved in the landing process, such as looking for a suitable landing spot and cancelling horizontal velocity during the terminal descent phase.

Furthermore, the landing vehicle is typically full of fuel, while the launched vehicle is almost empty. This affects the delta-V cost due to changes in mass. For example, the HLS Starship lunar lander needs to make five engine burns, using a total of 1300 tons of propellant to get to the lunar surface and back. The return journey requires less propellant because the vehicle is not carrying the entire mass of the propellant burned during the descent.

In summary, while the delta-v required for a manoeuvre is independent of the mass of the vehicle, the delta-V cost of landing is higher than that of taking off due to the increased energy requirements and the number of steps involved in the landing process. The delta-v budget is a crucial consideration in mission planning, as it helps determine the amount of propellant needed for a successful landing and return journey.

shunfuel

The HLS Starship lunar lander needs 450t of propellant to get to the lunar surface

The HLS Starship lunar lander is a part of NASA's Human Landing System program. It is designed to carry a payload to the lunar surface and bring it back up to lunar orbit. The success of the HLS program depends on the payload capacity of the Starship HLS.

The HLS Starship lunar lander requires 450t of propellant to get to the lunar surface from NRHO (near-rectilinear halo orbit) and back. The NRHO is a specific type of lunar orbit that requires 500 m/s delta V for each of the two engine burns to enter and exit. The HLS Starship lunar lander has to make five engine burns, using varying amounts of propellant for each burn.

The first burn, from LEO (low Earth orbit) to NRHO, uses 810t of propellant. The second burn, NHRO insertion, uses 67t. The third burn, from NRHO to the lunar surface, uses 255t of propellant. The fourth burn, from the lunar surface back to NRHO, uses 130t. The final burn, NRHO insertion, uses 16t of propellant. This leaves the HLS Starship lunar lander with 22t of propellant remaining, which is a 1.7% propellant safety margin. NASA may want a larger safety margin, such as 5%.

The HLS Starship lunar lander will need to be refueled in LEO before it can continue on its mission to the Moon. This refueling will be done by a flotilla of reusable Starship tankers that will transfer liquid oxygen and liquid methane to the HLS Starship lunar lander.

shunfuel

The HLS Starship lunar lander needs to make five engine burns to reach the lunar surface

The HLS Starship lunar lander has a dry mass of 78 tons and a payload of 20 tons. It can be refueled in LEO and has a total of 1300 tons of methalox in the main tanks after refueling. To get to NRHO from LEO, the HLS Starship needs to travel at a speed of 3.7 km/s using a fast transfer or 3.1 km/s using a slow transfer that takes a few months.

The HLS Starship lunar lander is planned to use high-thrust landing engines located in the mid-body section of the spacecraft to avoid plume impingement with the lunar regolith. These engines burn gaseous oxygen and methane instead of the liquid oxygen and methane used by the Raptors. The Raptors are used during launch and the majority of the landing and ascent phases.

The success of the HLS Starship lunar lander depends on its payload capacity. Due to its high dry mass, it cannot reach the Moon without first refueling in LEO. SpaceX must implement orbital refueling to complete the Artemis 3 mission.

Frequently asked questions

The Apollo 11 lander consumed 2200kg of fuel to get back to lunar orbit.

The descent of the Apollo Lunar Module to the moon's surface consumed 17,414kg of fuel.

The velocity of propulsion of the fuel must be calculated using the formula:

> v_f = (M / m) x v_e

where M is the initial mass, m is the final mass, and v_e is the escape velocity.

No, landing requires more energy than ascent due to the change in weight from fuel consumption.

Yes, there are text-based and 2D lunar lander games that simulate fuel usage, such as the Lunar Lander game.

Written by
Reviewed by

Explore related products

Share this post
Print
Did this article help you?

Leave a comment