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Problem Statement
How do you determine the right size for your parachute? We can apply an equation from the Rocket Equations Page to figure out the parachute needed for your rocket and how fast your rocket will be going during descent.
The rocket, under its parachute, will speed up toward the ground until the drag force on the chute is equal to the weight of the rocket. So to figure this problem out, we need to find equations for drag force and for the rocket's weight and set them to be equal.
We will try to find the diameter of parachute that brings the rocket down slowly enough that the rocket doesn't break when it hits the ground. How fast is that? It depends on how well you built your rocket, of course, along with where it lands - concrete will hurt more than field grass. If you simply drop your rocket from two feet high, it will hit the ground at a little over 7 mph, or approximately 3 m/s. We'd like to keep the speed to about that.
Solving the Problem
We will use the drag force, or "wind resistance force" equation, which is
FD = ½ r Cd A v2
Where
FD is the drag force
r (Greek letter "rho") is the density of air = 1.22 kg/m3
Cd is the drag coefficient
A is the area of the chute
v is the velocity through the air
Meanwhile, the weight of the rocket, otherwise known as the force of gravity (FG), is computed to be
FG = m g
Where
m is the mass of the rocket
g is the acceleration of gravity = 9.81 m/s2
Let's find when they're equal:
FG = FD
m g = ½ r Cd A v2
...and solving for chute area...
A = (2 m g) / (r Cd v2)
Now the chute area, in terms of the chute diameter, is A = p D2 / 4, so the chute diameter is
D = sqrt(4 A / p).
The Answer
Combining the two equations above for A & D leads us to the final form of the chute equation as we will use it:
D = sqrt( (8 m g) / (p r Cd v2) )
Where
D is the chute diameter in meters
m is the rocket mass in kilograms
g is the acceleration of gravity = 9.8 m/s2
p is 3.14159265359
r is the density of air = 1.22 kg/m3
Cd is the drag coefficient of the chute, which is 0.75 for a parasheet (flat sheet used for a parachute, like Estes rockets), or 1.5 for a parachute (true dome-shaped chute).
v is the speed we want at impact with the ground (3 m/s or less)
Some Examples
Model Rocket
Let's size a parachute for an Estes Big Bertha.
m = 62.3 g = 0.0623 kg (from the Estes catalog)
Cd = 0.75 (since this is a parasheet)
the rest of the variables are as above, so...
D = sqrt( (8 m g) / (p r Cd v2) ) = sqrt( (8*0.0623*9.81) / (3.14*1.22*0.75*32) ) = 0.435 m
...which is equal to 17 inches. This explains why the Big Bertha comes with an 18 inch chute.
High-Power Rocket
We'll size a parachute for my LOC V2, which weighs in at 8 pounds even, or 3.6 kg.
m = 3.6 kg due to all the extra stuff I've added
Cd = 1.5 because the rocket uses a true domed parachute
v = 5 m/s I'm increasing v because this rocket's going pretty high and I don't want it to take forever to come down. This is the equivalent to a four-foot drop (ouch).
D = sqrt( (8 m g) / (p r Cd v2) ) = sqrt( (8*3.6*9.81) / (3.14*1.22*1.5*52) ) = 1.4 m
...which is a 4 foot 8 inch parachute. Pretty big. In reality I'm using a RocketMan R7C, which is about that size.
Finding Descent Velocity
Note that we can easily find the descent velocity, given the chute diameter, by simply rearranging the above equation to get
v = sqrt( (8 m g) / (p r Cd D2) )
On August 6, 2012, the Mars Science Laboratory rover, Curiosity, successfully landed on the surface of Mars. The Entry, Descent and Landing (EDL) sequence was designed using atmospheric conditions estimated from mesoscale numerical models. The models, developed by two independent organizations (Oregon State University and the Southwest Research Institute), were validated against observations at Mars from three prior years. In the weeks and days before entry, the MSL "Council of Atmospheres" (CoA), a group of atmospheric scientists and modelers, instrument experts and EDL simulation engineers, evaluated the latest Mars data from orbiting assets including the Mars Reconnaissance Orbiter's Mars Color Imager (MARCI) and Mars Climate Sounder (MCS), as well as Mars Odyssey's Thermal Emission Imaging System (THEMIS). The observations were compared to the mesoscale models developed for EDL performance simulation to determine if a spacecraft parameter update was necessary prior to entry. This paper summarizes the daily atmosphere observations and comparison to the performance simulation atmosphere models. Options to modify the atmosphere model in the simulation to compensate for atmosphere effects are also presented. Finally, a summary of the CoA decisions and recommendations to the MSL project in the days leading up to EDL is provided.
The most recent planetary science mission to Mars is the Mars Science Laboratory (MSL) with the Curiosity rover, which launched November 26, 2011 and landed successfully at Gale Crater on August 6, 2012. This rover was the first use at Mars of a complete closed-loop Guidance,
Navigation, and Control (GN&C) system, including guided entry with a lifting body (via center of gravity offset) to greatly reduce targeting errors during the Entry, Descent, and Landing (EDL) phase. Hypersonic entry guidance enables the entry body to fly out the remnant delivery error from the final Trajectory Correction Maneuver (TCM) as well as other sources, resulting in less than a 25km20km landing error relative to the Gale Crater landing target.
MSL used a supersonic Disk-Gap-Band (DGB) parachute during its EDL sequence. Thus far, every robotic mission to Mars has used heritage from the deceleration technologies developed during the Viking era in the 1960s. The MSL DGB parachute had a 33% larger diameter than the
Viking parachute due to the heavier weight of the MSL spacecraft during EDL.
The high-fidelity EDL simulation has over 30;000 parameters that must be specified for proper operation. A large subset of these parameters, over 90% of the total, were either managed by an EDL configuration control spreadsheet or were parameters that were compiled into the software.
originally posted by: yhin999
I've never heard Andrew Basiago claim he has travelled a million years into the past. And there is no need to attack me personally and call me stupid. I'm just discussing the topic at hand, I don't call you stupid for believing in NASA's lies. Perhaps it is you who needs to switch their brain on.