A customer asked if we could use a passive UHF RFID (Ultra-High Frequency Radio Frequency Identification) system to monitor if employees crossed certain line in their warehouse. Because of the industry they were in, they could be assessed steep fines when unauthorized people entered restricted areas. After hearing about this request from my engineers, I jumped in because it gave me the opportunity do work on some real, honest to goodness, mathematics.
In my former life as a PhD student at UC San Diego, I was privileged to be able to work on math problems every day. However, in my current position as the CEO of Telaeris, the occasions to use higher math are few and far between. But boy – do I ever love math! And because we solved the problem for our customer, you get the solution for free, just by reading.
Looking at our customer’s problem initially, we decided that because of the high ceilings in the warehouse, we would likely have the reader antennas mounted in the floor.
سوال ما که باید پاسخ داد این بود:
RFID خوانده می شود تا چه حد از خط خارج شود؟
We chose wide RFID antennas, to minimize the number of antennas that would be used. Each antenna had beam width of 45 degrees. If employee badges are worn around the neck, the badges should hang about 4 feet above the ground. This is where the math comes in. We need to set up a series of equations to calculate the distance X from the line that the reader has to be installed. The diagram is shown below.
من چند سالی را به کلاس من مثلث من در دبیرستان La Salle در Pasadena با آقای Uejima می کشم. با توجه به یک طرف و یک زاویه از مثلث راست، ممکن است برای تمام طرفها و یا زوایای دیگر حل شود.
ابتدا باید زاویه α را بدست آوریم. از آنجا که α + θ یک زاویه راست (90 °) است و می دانیم که عرض کامل پرتو 45 ° می تواند برای α با معادلات زیر حل کند.
Then from the dark recesses of my mind an acronym came forth calling out “TOA….TOA…TOA” – tangent equals opposite over adjacent! With this, I was able to set up the equations to solve directly for the distance X.
Of course, when we use to do this at school, we had trig tables in the back of our math books. Today, I just asked my cell phone “what is the tangent of 67.5 degrees” and was rewarded with the value for my calculations.
پاسخ برای فاصله از خط محاسبه می شود پا 1.66 یا 20 اینچ دور از خط. این باعث می شود رد نشوید محدوده و نه تنگ و باریک.
I love the fact that with just a little bit of math and common sense, we are able to quickly characterize how a system should theoretically behave. Of course, this doesn’t account for the way passive RFID می تواند منعکس کننده و گزاف گویی باشد، اما برخی از مسائل تنها می تواند با آزمایش در این زمینه حل شود.
The next time we get into math, I hope to be able to discuss multi-variable optimization of real time location systems….but somehow I think I will have a much smaller audience for that article!