How complex is a Boeing 747 Airplane ?
- In this post, I propose a very simple ballpark estimate of the complexity of a Boeing 747 airliner.
- I am interested in your thoughts, your input and constructive criticism.
First-pass lower-bound complexity estimate (Boeing 747 airliner)
- A Boeing 747 has 6 million parts (source: Boeing Corp.).
- Assume that all of the parts are simple objects that are interchangeable, but which need to be placed in specific x-y-z coordinate positions, with specific angular theta-x theta-y theta-z values (with respect to a uniform airplane-construction frame-of-reference).
- So, each part has 6 degrees of freedom (6 independent parameters).
- How many bits of information do I need to specify, in order to place the 6 million parts in correct positions (x,y,z, theta-x, theta-y, theta-z) to assemble a 747 airliner?
- Now, each part needs to be placed in position with a specific accuracy (which depends on the part, and its function in the plane). These specific-accuracy values will be different for different parts.
- For ease of calculation, let’s assume that the range of coordinate values (that we choose to consider) for placement of a part is 128 times the placement-accuracy value needed for that part…
- Example: If an object needs to be fitted into the 747 airplane, with a lateral placement accuracy of 1 millimeter, we assume that the range of possible values that we consider as options for placement of that part are 128 steps of that placement-accuracy-value (= 128 millimeters = 12.8 centimeters = less than 6 inches). I am choosing to do this in order to make the calculation easier … and this simplifying assumption is intended to give us a ball-park lower-bound complexity measure of the 747 airliner…
- On the other hand, if an object needs to be fitted into the 747 airplane, with a lateral placement accuracy of 1 inch, we assume that the range of possible values that we consider as options for placement of that part are 128 steps of that placement-accuracy-value (= 128 inches). I am choosing to do this in order to make the calculation easier … and this simplifying assumption is intended to give us a ball-park lower-bound complexity measure of the 747 airliner…
- Another Example: If the part needs to be placed with an angular rotational accuracy of 2 degrees (about the x-axis for instance), we consider the range of possible values to be 128 steps of this angular accuracy = 256 degrees.
- Based on these simplifying assumptions, we find that we need 128 values to determine the possible positions taken by one parameter. 128 values requires 7 bits to store (since 2^7 = 128). This is a lower-bound estimate.
- So, for any one part (that is used to fabricate the 747 airliner), we need to specify 6 parameters (x position, y position, z position, theta-x value, theta-y value, theta-z value), and each parameter can take 128 values (multiples of the placement accuracy of each part).
- 1 parameter needs 7 bits of information (128 values).
- 6 parameters need 6x7 = 42 bits of information.
- This means that placement of one generic part needs 42 bits of information (since placement of one part requires 6 parameters to be specified).
- And therefore, placement of 6 million parts will require 252 million bits of information (42 bits per part x 6 million parts = 252 million bits = 2.5E8 bits = approx 3E8 bits).
- This appears to me to be a lower-bound estimate of the complexity of a Boeing 747 airliner.
Second-pass lower-bound complexity estimate (Boeing 747 airliner)
- Next, I present an attempt to refine the first-pass estimate mentioned above.
- The basic reasoning is the same as the estimate above. The refinement is to include an estimate of the dimensions of the parts.
- Given: 6 million parts.
- Let’s say that these 6 million parts are composed of duplicates of a smaller number of distinctively-different parts. Let’s say there are 6000 distinctively-different parts (with 1000 copies of each) which add up to give us the 6 million parts used to build the Boeing 747 airliner.
- A simplifying assumption. Let’s say that each of these 6000 distinctively-different parts is completely determined by its length dx, width dy, and height dz. This is obviously an extremely simplifying assumption.
- We would have to add the added complexity (of the distinctively-different parts’ dimensions) to the first-pass complexity-estimate calculation above. Let’s see how much this added complexity is (in information bits).
- Consider ONE distinctively-different part. It has 3 parameters (dx, dy, dz) in addition to the 6 parameters considered in our first-pass calculation.
- Just as we did in the first-pass estimate, we will now use an estimate of 128 values as the range of values each parameter can take (i.e., the range being 128 times the dimensional-accuracy needed for this part to fit to make the Boeing 747).
- So, dx can take 128 values (128 multiples of dx-required-dimensional-accuracy), dy can take 128 values, dz can take 128 values.
- 128 values requires 7 bits to store (lower-bound estimate).
- So, given 6000 distinctively-different parts (DDP), 3 added parameters per part, 7 bits per parameter, we come up with the 6000 DDP requiring 126000 bits of information (6000 x 3 x 7 bits = 126000 bits = 1E5 bits).
- Now, since we have the 6000 DDP duplicated 1000 times, and each of the duplicates are identical with one of the DDP, we just need to store the number of duplicates for each kind of part = 1000 numbers, each of which has a range of 1-1000 (assuming each DDP part can now vary from 1 to 1000 in number of duplicates).
- To store 1000 takes 10 bits (2^10 = 1024). To store 1000 such numbers then takes 10 x 1000 = 10,000 bits = 1E4 bits.
- This does not change our 1E5 estimate for the 6000 distinctively-different parts (because 1E5 + 1E4 is approximately = 1E5).
- So the additional complexity that arises from our second-pass calculation is 1E5 bits.
- To obtain the total (lower-bound) complexity for a Boeing 747 airliner from our second-pass complexity-calculation, we need to add in this additional 1E5 bits (to the complexity estimate from the first pass calculation, i.e., 3E8 bits).
- 3E8 bits + 1E5 bits = 3E8 bits (approx).
- So, our estimate for the complexity of the Boeing 747 Airliner has not changed.
Bottom-line: Lower-bound complexity estimate of a Boeing 747 airliner
- Based on the reasoning presented above, for both first-pass and second-pass estimations, we estimate the lower-bound complexity of a Boeing 747 airliner to be 3E8 bits.
I would be interested in recognizing any strengths/ weaknesses of the reasoning above,
and any improvements to the calculations or methodology.
- Feel free to email me your thoughts, comments, and constructive criticism.
- Wishing you Peace and Love through Jesus Christ.