From f4337dff14b501a6e61961c33b4f842670fd2979 Mon Sep 17 00:00:00 2001 From: Andrew Ning Date: Wed, 13 Nov 2024 19:22:25 -0700 Subject: [PATCH] next hw --- atom.xml | 2 +- feed.xml | 2 +- me415/schedule/hw8/index.html | 6 +- me415/schedule/hw9/index.html | 130 +++++++++++--------------- me415/schedule/index.html | 2 +- me415/schedule/tanks.png | Bin 166190 -> 132904 bytes me415/schedule/traj.dat | 168 ++++++++++++++++++++++++++++++++++ 7 files changed, 225 insertions(+), 85 deletions(-) create mode 100644 me415/schedule/traj.dat diff --git a/atom.xml b/atom.xml index 8d06c33..7c30c55 100644 --- a/atom.xml +++ b/atom.xml @@ -4,7 +4,7 @@ FLOW Lab - 2024-11-13T13:57:12-07:00 + 2024-11-13T19:22:19-07:00 http://flow.byu.edu Andrew Ning diff --git a/feed.xml b/feed.xml index db88feb..27db033 100644 --- a/feed.xml +++ b/feed.xml @@ -1 +1 @@ -Jekyll2024-11-13T13:57:12-07:00http://flow.byu.edu/feed.xmlFLOW LabFlight, Optimization, and Wind LaboratoryAndrew NingOptimization Book Available2021-10-15T00:00:00-06:002021-10-15T00:00:00-06:00http://flow.byu.edu/posts/opt-book]]>Andrew NingBEM Paper2021-07-30T00:00:00-06:002021-07-30T00:00:00-06:00http://flow.byu.edu/posts/bem-paper]]>Andrew NingEduardo Research Update2021-03-01T00:00:00-07:002021-03-01T00:00:00-07:00http://flow.byu.edu/posts/eduardo-latest]]>Eduardo AlvarezReformulated VPM2021-02-01T00:00:00-07:002021-02-01T00:00:00-07:00http://flow.byu.edu/posts/reformulated-vpm]]>Eduardo AlvarezOptimization Book Announcement2021-01-20T00:00:00-07:002021-01-20T00:00:00-07:00http://flow.byu.edu/posts/optimization-book]]>Andrew NingPJ Defense2020-09-30T00:00:00-06:002020-09-30T00:00:00-06:00http://flow.byu.edu/posts/pj-defense]]>Andrew NingVPM Paper2020-08-30T00:00:00-06:002020-08-30T00:00:00-06:00http://flow.byu.edu/posts/vpm-paper]]>Eduardo AlvarezAirborne Wind with Vortex Particle Method2020-08-16T00:00:00-06:002020-08-16T00:00:00-06:00http://flow.byu.edu/posts/wind-harvesting]]>Judd Mehr and Eduardo AlvarezEduardo’s Past Three Years2020-08-10T00:00:00-06:002020-08-10T00:00:00-06:00http://flow.byu.edu/posts/eduardo-three-years]]>Eduardo AlvarezFLOWUnsteady in Google Drive2020-08-02T00:00:00-06:002020-08-02T00:00:00-06:00http://flow.byu.edu/posts/google-drive-vpm]]>Eduardo Alvarez \ No newline at end of file +Jekyll2024-11-13T19:22:19-07:00http://flow.byu.edu/feed.xmlFLOW LabFlight, Optimization, and Wind LaboratoryAndrew NingOptimization Book Available2021-10-15T00:00:00-06:002021-10-15T00:00:00-06:00http://flow.byu.edu/posts/opt-book]]>Andrew NingBEM Paper2021-07-30T00:00:00-06:002021-07-30T00:00:00-06:00http://flow.byu.edu/posts/bem-paper]]>Andrew NingEduardo Research Update2021-03-01T00:00:00-07:002021-03-01T00:00:00-07:00http://flow.byu.edu/posts/eduardo-latest]]>Eduardo AlvarezReformulated VPM2021-02-01T00:00:00-07:002021-02-01T00:00:00-07:00http://flow.byu.edu/posts/reformulated-vpm]]>Eduardo AlvarezOptimization Book Announcement2021-01-20T00:00:00-07:002021-01-20T00:00:00-07:00http://flow.byu.edu/posts/optimization-book]]>Andrew NingPJ Defense2020-09-30T00:00:00-06:002020-09-30T00:00:00-06:00http://flow.byu.edu/posts/pj-defense]]>Andrew NingVPM Paper2020-08-30T00:00:00-06:002020-08-30T00:00:00-06:00http://flow.byu.edu/posts/vpm-paper]]>Eduardo AlvarezAirborne Wind with Vortex Particle Method2020-08-16T00:00:00-06:002020-08-16T00:00:00-06:00http://flow.byu.edu/posts/wind-harvesting]]>Judd Mehr and Eduardo AlvarezEduardo’s Past Three Years2020-08-10T00:00:00-06:002020-08-10T00:00:00-06:00http://flow.byu.edu/posts/eduardo-three-years]]>Eduardo AlvarezFLOWUnsteady in Google Drive2020-08-02T00:00:00-06:002020-08-02T00:00:00-06:00http://flow.byu.edu/posts/google-drive-vpm]]>Eduardo Alvarez \ No newline at end of file diff --git a/me415/schedule/hw8/index.html b/me415/schedule/hw8/index.html index 1201bbb..346f5a1 100644 --- a/me415/schedule/hw8/index.html +++ b/me415/schedule/hw8/index.html @@ -11,7 +11,7 @@ - HW 8 · ME 415 + HW · ME 415 @@ -87,7 +87,7 @@

- +

HW 8

due 11/13/2024 before midnight via Learning Suite @@ -153,7 +153,7 @@

HW 8

-

The fuel tanks and rocket body are made of aluminum. Note that a stacked configuration is used and that about 10 meters of extra length is required below the tanks for the engines. As shown on the right, it is easiest to estimate the required tank size by assuming that the tanks are cylinders and then add on about 3 meters per tank to account for the fact that the round end caps will need to be longer than a pure cylinder and that there will be some ullage volume (that means the tanks won’t be 100% filled). For simplicity, I’d treat the diameter of the tanks as the same as that of the rocket body (it’s a really small difference). Note that the cylindrical tanks are meant to have the same volume as the rounded tanks (see right-most figure). So for a fixed volume they will be shorter (which is why we add in the extra length), but the surface area should be roughly the same. In other words, the added 3m length per tank should only affect the total length calculation of the stage, it should not affect the structural mass calculation.

+

The fuel tanks and rocket body are made of aluminum. Note that a stacked configuration is used and that about 10 meters of extra length is required below the tanks for the engines. As shown on the right, it is easiest to estimate the required tank size by assuming that the tanks are cylinders and then add on about 3 meters per tank to account for the fact that the round end caps will need to be longer than a pure cylinder and that there will be some ullage volume (that means the tanks won’t be 100% filled). For simplicity, I’d treat the diameter of the tanks as the same as that of the rocket body (it’s a really small difference).

Because the structural mass depends on the propellant mass, and the propellant mass depends on the structural mass, an iterative process is required (i.e., root finding). If you’re struggling to know if you’re on the right track, because this is an actual rocket, you could start with the known propellant mass and work your way through the equations checking your numbers against the actual rocket, then fine tune from there.

diff --git a/me415/schedule/hw9/index.html b/me415/schedule/hw9/index.html index f720831..9589987 100644 --- a/me415/schedule/hw9/index.html +++ b/me415/schedule/hw9/index.html @@ -11,7 +11,7 @@ - HW 9 · ME 415 + HW · ME 415 @@ -87,84 +87,56 @@

- -

HW 9: Rockets

- -

due 12/6/2017 before midnight via Learning Suite -50 possible points

- -

All of these exercises will be done in class (though some of you may need a little extra time outside of class to finish up). I’d like to give you practice with rocket analyses, while still preserving your out of class time for finishing up your plane and report.

- -
    -
  1. -

    Basic Sizing of a Rocket Engine. Some parameters for a liquid-fueled rocket engine are given below:

    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    \(\gamma\)ratio of specific heats for combustion gas mixture1.2
    \(M_w\)molecular weight of combustion gas mixture12 (g/mol)
    \(T_{Tc}\)combustion (total) temperature3500 K
    \(P_{Tc}\)combustion (total) pressure20 MPa
    \(I_{sp}\)required specific impulse at altitude400 seconds
    \(T\)required thrust at altitude2 MN
     nozzle type80% bell nozzle
    \(\sigma_c\)max allowable stress in combustion chamber wall55 MPa
    - -

    Design for peak efficiency at an altitude of 12.5 km (shortly after max-Q). The required thrust and specific impulse apply at this altitude.

    - -

    Determine/design the following:

    - -
      -
    • the areas (3) at the end of the combustion chamber, throat, and exit.
    • -
    • the lengths (3) of the combustion chamber, the converging, and diverging sections of the nozzle.
    • -
    • the wall thickness (1) of the combustion chamber assuming a thin-shell cylindrical combustion chamber.
    • -
    • Draw your nozzle to scale.
    • -
    - -

    Note: These specs correspond to the Space Shuttle Main Engine so you can check some of your numbers (though don’t expect them to be exactly the same, there are important boundary layer losses and multiphase flow losses on a nozzle that we are neglecting).

    -
  2. -
  3. -

    Basic Sizing/Performance of a Rocket. The worksheet is available online. I’ve already laid out the methodology so you don’t need to repeat it here. Just report the four critical values, and include a brief discussion on any lessons learned.

    -
  4. -
- - - - + +

HW 9

+ +

due 11/20/2024 before midnight via Learning Suite +15 possible points

+ +
+ +

This problem uses the same rocket from the previous homework. In this case we are interested in the flight trajectory. The Saturn V does not fly at a straight angle during the first stage and so it would be difficult to provide an accurate estimate using the closed-form rocket equation. Instead, we need to use numerical integration. Though we will still ignore drag in this analysis.

+ +

As mentioned the heading angle changes significantly throughout the flight. I fit a curve to postflight trajectory data and computed the heading angle as a function of time during stage 1. Note that \(\theta = 0\) corresponds to vertical flight:

+ + + +

\(\theta = p_1 \arctan\left(p_2 t^{p_3}\right)\) +where +\(p_1 = 0.866, p_2 = 2.665 \times 10^{-5}, p_3 = 2.378\)

+ +

Other parameters you will need:

+ + + + + + + + + + + + + + + + +
thrust35.1 MN
total rocket mass\(2.97 \times 10^6\) kg
specific impulse283 s
+ +

You could solve this using any ODE solver (e.g. scipy.integrate.solve_ivp in python), or you could write a basic forward Euler method. This means that you setup a time vector, and a starting point for \(V, m, z, x\), and then execute a for loop. At iteration (\(i\)) you update those four values using data from the previous iteration (\(i - 1\)). For example, using the last ODE (and setting \(\Delta t = t^{(i)} - t^{(i-1)}\)):

+ +\[x^{(i)} = x^{(i-1)} + V^{(i-1)}\sin\theta^{(i-1)} \Delta t\] + +

Report the following. Be sure to clearly show your work and assumptions.

+ + + +
    +
  • Plot the trajectory with forward distance on the \(x\)-axis and altitude on the \(y\)-axis. (I tabulated the actual flight data if you are interested in comparing, first column is the forward distance, and the second column is the altitude).
  • +
  • Your final velocity, altitude, and forward distance.
  • +
+
diff --git a/me415/schedule/index.html b/me415/schedule/index.html index 06cc447..22295af 100644 --- a/me415/schedule/index.html +++ b/me415/schedule/index.html @@ -394,7 +394,7 @@

Schedule

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