Skip to main content
Physics LibreTexts

13.2: Mars Lander

  1. Last updated
  2. Save as PDF
  • Page ID
    17827

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Project Goals

    • Use hands-on experience to reinforce physics concepts covered so far
    • Jump cognition levels to create
    • Practice critical thinking and the scientific process
    • Have fun

    Project Description

    Lander Delivery

    Welcome to the first briefing for the touchdown redundancy team. Please play close attention because I am going to throw a lot of information at you.

    Now, as you are aware the sky crane has emerged as the most practical method of delivering relatively massive payloads to the Martian surface. For a brief recap of that system watch the following video:

    hqdefault-21.jpg

    A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/bodyphysics/?p=3349

    As we know, the sky crane system successfully delivered the curiosity rover to Mars, an important step in getting this historic point, where we are now in mission design phase for the Human Exploration of Mars. Several sky crane systems will be used to deliver supplies, equipment and the return rocket ahead of the human mission.

    Your Task

    We calculate a low failure probability for the sky crane, but we also estimate that the large majority of that probability is concentrated during the time when the crane is within 14 m of the surface.

    We know humans and equipment can only survive forces up to a certain threshold. Therefore, this team will design a lander which will prevent accelerations above the safety threshold for drops up to 14 m on Mars. This will ensure that the humans and critical equipment survive an unexpected drop to the Martian surface with no adverse effects.

    The system you design to accomplish this must not rely on any other system, which would create a redundancy spiral, and that includes any electronics systems. (Therefore a parachute deployment system is not acceptable).The system must be built into the structure of the lander itself. You will be designing a Mechanical Acceleration Suppression System, or M.A.S.S.

    Design and Testing Parameters:

    In order to generate a diversity of design ideas the team will be split into groups. I want hands-on contributions from all members, so groups cannot be bigger than three. I also want us checking and double-checking each other’s work, so no groups smaller than two.

    Each group will design a system, build a model, and we will test them in our free-fall facility here in the building. The model test subjects and equipment we will use will be three raw eggs.

    We must recognize that g on mars is only about 3.8 m/s/s compared to 9.8 m/s/s on Earth so you will calculate a new drop height for testing our models here on Earth.

    The model lander must fall straight down from the calculated height and land within a 25 cm x 25 cm area to ensure that it lands in the safe location identified by the sky crane imaging system. (Therefore a parachute system is not acceptable).

    Due to the fuel requirements and cost of launching mass into space, you are limited to a total mass of 500 g for your model lander system, including the payload (eggs).

    Due to the size limitations of the spacecraft you are limited to a total size of 20 cm wide x 20 cm long by 30 cm high for your model lander system.

    You are also limited on your design budget. In order to maximize the efficiency of taxpayer dollars for space exploration you are limited to the following materials, with associated costs and your total cost cannot go above 500 USD.

    Glue: No cost

    Paper: 4 USD/gram

    Cardboard: 6 USD/gram

    Wood (Popsicle sticks) 10 USD/gram

    Aluminum Foil: 25 USD/gram

    Presentation and Testing:

    You will give the class an 8 minute presentation on your model that will include the following sections:

    1. Model design features
    2. Physics concepts and reasoning behind your design
    3. Materials cost breakdown for your model
    4. Difficulties and solutions/redesigns during your project

    Model Evaluation (Grading)

    C-grades will be earned by:

    1. correctly completing and submitting the guide calculations worksheet
    2. fully participating in the design-build process
    3. keeping your design within budget limitations
    4. contributing to your group presentation.

    B-Grades will be earned by doing the above plus:

    1. landing completely within the designated area
    2. preventing damage to the test subject (egg).

    A-Grades will be earned by doing all of the above plus:

    1. keeping within mass and size limitations

    Guide Calculations:

    Drop Height, Speed, and Acceleration

    Using our knowledge of conservation of mechanical energy determine the Earth drop height we need to provide the same impact speed as a 14 m drop on Mars:

    We want to limit the peak acceleration felt by the cargo to 10 g. The humans and equipment will be strapped tightly to the lander frame so the lander frame must not accelerate at more than 10 g. What is this acceleration in m/s/s?

    Impact Force

    Assuming your lander + payload have the maximum 300 g mas, calculate the maximum net force that can be applied to the lander on touchdown without exceeding the threshold acceleration:

    Draw a free body diagram of the lander during impact

    Determine the peak normal force that can be applied to your model by the ground in order to prevent such an acceleration. This is your safety threshold force.

    You may use force plate to test version of your models and see how they react to forces of various sizes.

    Impact Duration

    Use the lander mass and impact speed to calculate the change in momentum of the lander upon impact.

    If you design your lander to keep the average net force applied on impact to be less than 1/3 of the safety threshold, then the peak force will likely not exceed the safety threshold. Draw a F vs. t curve for the impact that illustrates this idea.

    If you were to achieve this average force value of 1/3 the peak force threshold, then over what time would you need to spread the impact?

    What design features will you implement to spread out the impact duration?

    Testing

    Record the dimensions of your lander here:

    Width:________Length:______Height:________

    Record the mass of the lander here:________

    Record the masses and total cost of various materials used:

    Record the total cost of your lander here:______

    Did your payload survive without damage?

    This page titled 13.2: Mars Lander is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Lawrence Davis (OpenOregon) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.