AirVenture Oshkosh: Rutan

 DAY 4 (July 28th) 

Burt Rutan had a forum at the museum today. It wasn't a serious lecture, just a light storytelling from this great man. He simply asked the crowd what we'd like to hear. Everyone was ready for a good story. He started, telling us of his favorite design -- SpaceShipOne. Indeed it was a most magnificent idea to have a it "feather" itself to reduce speed then touch down at the airport like all other airplanes.


I admit that I've known nothing about Rutan before AirVenture. I've heard about SpaceShipOne, but that was about as far as it goes. Upon hearing his story however, I am sure he is more than just a super brilliant aircraft designer. What with his old age and heart conditions, he is still flying! (He performed in the air show that afternoon.) How much enthusiasm must the man have! I like what how he build his first spacecraft himself. because people said, "Nay, that's not going to work." and were afraid to build it. And look! It did flew! Without using great big fuel cells, an "airplane" was able to go to space and back again!


How I wished I was there when the White Knight carried it up to the sky! To feel the suspense and to wish, over and over again, that it will be a safe and successful trip. Watching the documentary, seeing the M&M's flying in the cockpit, so much has gone though my head. It seems that my dream of general spaceflight will happen in my time. Perhaps even going to other planets instead of just orbiting around the earth. What if Issac Asimov's story comes true? It does not seem that impossible anymore. Even when I doubt it before, I am confident now. 

[Problem] A Pin In Constrained Motion

QUESTION

A pin is constrained to move in a circular slot of radius 64mm. At the same time a slotted bar also constrains the pin to move down with a constant velocity of 4mm/s as shown. What is the magnitude of the acceleration of the pin for the position shown?

SOLUTION

1. The time it takes for the pin to move to the position is:

2. The position of the pin can be expressed as follows:

3. the pin is moving downward in a costant acceleration, therefor we know that the magnitude of the acceleration of the pin comes from the sideways movement, namely x-direction movement. Therefore, we can re-write the equation as: 

and, taking the differential, we get: 

taking the differential again, we get:

4. Substituding the time t we have caculated in 1., we get the position x. From t and x we can obtain the vlocity (dx/dt). And finally, the acceleration (d2x/dt2).

NOTE

When I first saw the question my immediate thought was to use relative motion. I had a hard time finding the relationship between the pin and the slotted bar or the center of motion. Then I thought I could do it by using energy conservation. But then I'd have to first calculate the velocity of the pin and then calculate the kinematic energy and make life hard. The above solution, using differentials, is by far the most direct and foolproof way I can think of. It does, nonetheless, involve quite some calculating and reducing, which might more easily result in mindless mistakes. So I wonder if it could be solved without having to take the differentials and use the Newton's second law instead? 

[C/C++] Programing in Ubuntu (by commend line)

1. Needs to install the compiler: Which includes the libc-dev, gcc, g++, make and dpkg-dev which should suffice for C/C++ programming.

      Commend line:  sudo apt-get install build-essential 

2. In a chosen folder, right click and choose "Create Document > Empty File" to create a file. Name it filename.c.

3. Double click the file to open it. Write your program in the file and save.

4. Open terminal. Switch to the file directory in which the file is in.

      Commend line:  cd ./foldername1/foldername2 

5. Compile the file.

      Commend line(for C):  gcc filename.c 

      Commend line(for C++):  g++ filename.c 

6. Show output.

      Commend line:  ./a.out