Remember the space shuttle? One of the original goals for the shuttle program was to build a vehicle that could launch into orbit, have a quick turnaround time, and launch again. Unfortunately, it didn’t work out as well as planned. It usually took two months to process the shuttle before its next launch.
The idea of the Blue Origin New Shepard is to create a spacecraft that is more like an airliner. Another important aspect of a reusable spacecraft is to not destroy a big part of it on every launch. But to save the first stage of the rocket, it must land on Earth instead of just falling into the ocean.
It looks like Blue Origin has solved one of these problems. It has successfully relaunched one of its first stages. Even though the payload didn’t reach orbit, it’s still an impressive first step.
Acceleration During Launch
Now it’s time to do what I do—analyze the motion of the rocket. Several parts of the video have interesting motions, but let me stick with the initial launch. Of course I use the Tracker Video Analysis program (it’s free and awesome) to get position and time data from the video.
Two issues must be addressed before obtaining data. First, the video requires something to set the scale. My Google-Fu failed me and I didn’t find a direct description of the size of the New Shepard. However, the Blue Origin page does show the first stage alongside the silhouette of a man. Also, a silhouetted man in another picture indicates he is 6 feet tall. That’s what I need. From that, I get a height of the first stage (from landing gear to top) of about 15.5 meters.
Second, I must deal with the panning and zooming camera in the video. The easiest way to correct for the camera motion is using Tracker Video’s calibration point pairs. Basically, you mark two locations on the background of the video to track both zooming and the coordinate motion. Here is a quick tutorial if you are interested.
Now it’s a simple matter of marking the top of the rocket in each frame. With this, I get the following position-time data.
Since the data looks fairly quadratic, I can fit a function to find the acceleration. Recall the following kinematic equation for constant acceleration.
From this equation you can see that the constant term in front of the t2 term is half of the acceleration. Looking at the fitting equation in the plot, the launch acceleration of the New Shepard is about 3.74 m/s2 (assuming my scale is correct). Yes, this doesn’t seem like a large acceleration—but it’s not bad. A small acceleration over a long time interval can lead to high velocities. Also, as the rocket uses fuel and becomes lighter, the acceleration can be greater.
Acceleration on Landing
Perhaps the landing portion of the spacecraft’s flight is more interesting. It’s also easier to analyze because the camera remains stationary during the first part of the landing. Let’s get right to the data. Here is a plot of the vertical position of New Shepard during the landing.
I fit two functions to the data. For the first part, the spacecraft is moving at a fairly uniform speed. Using a linear fit, the slope of the line would be the spacecraft vertical velocity. From this you can see that it is traveling at 77.8 m/s (174 mph). That’s quite a bit faster than I would expect—but what do I know? I’m not a rocket scientist.
Once the spacecraft begins to slow, it appears to have a constant acceleration. Again I can fit a quadratic function to find the acceleration. In this case, it has an acceleration of about 19.6 m/s2.
But why do I need to even find these velocities and accelerations? I don’t—it’s just for fun.Go Back to Top. Skip To: Start of Article.