Using Audacity Recording Software to Find Bullet Velocity at Various Distances

Part 1: Proof of Concept By Max and Phildog http://nitricacid.blogspot.com pdf version October 27, 2005 By using audio recording software such as Audacity, it should be possible to calculate the speed of bullets fired at metal targets by measuring the time it takes the sound of impact to reach the microphone after the bullet has been fired. This would be useful as both a basic chronograph, and for ballistics studies of various bullet shapes. Since we had a weekend free, we decided to give the idea a test run. This was our first attempt, and it was intended strictly as a proof of concept. Like all good first experiments, we found two things we did wrong for each thing we did right. The idea was simple. Since the speed of sound through air is dependent only on temperature, we should be able to record the sound of a bullet impacting on a metal target at a known distance, and subtract the time it took the sound of impact to travel back, to get the speed of a bullet over the distance. All we needed were some big chucks of metal, a good private shooting range, a tape measure, and a recording platform.

The white, blue, and black barrels holding the plates are 35, 70 and 100 yards away, respectively. Audacity is a full-featured open-source audio recording software. It came in especially handy for our experiment since it features a spectral waveform analysis tool that helped us tease out the impact sounds from other reflected sounds on the range. Here is the waveform and spectrum from a Marlin 30-30 lever action rifle impacting the first metal plate 35 yards away: Here's an mp3 of the sound. The bullet’s ringing impact on the metal plate is heard clearly and is discerned in the spectrogram by the persistence of audio peaks at certain frequencies as the ringing trails off. The other peaks in the spectrogram are echoes of the shot and impact bouncing off other objects in the field. Using the select feature in Audacity, it is possible to zoom in and measure the precise instant the bullet left the barrel, and when the impact sound returned to the microphone. For the above example, a time of 0.1575 seconds was recorded. Now, a word about the speed of sound. According to Wikipedia, the speed of sound in air varies only with temperature according to this formula: Speed (m/s) = 331.5 + 0.6*Temp(°C) So for our purposes, the flight time of the bullet would be the total time minus the time it took the sound to come back from the target. We then divide the distance by the flight time: B_s = D_target /(T_total – (D_target / (331.5+0.6*°C))) where B_s is the speed of the bullet, D_target is the distance to the target, and T_total is the total time from when the gun was fired and the impact was heard. Since we were at a high altitude on a clear, sunny day, the air temperature was changing during the experiment. Since we didn’t have a thermometer with us, we got weather station data from Mesowest and built a temperature curve: The only thing left to do was to listen to all the recordings and get the impact times. Here’s a table of our final results: A copy of the whole spreadsheet is available at the bottom. Conclusion Obviously, we have a lot of work to do. The first challenge, of course, is finding a private range. Since we were shooting with friends, it was tough to keep the whole range quiet while we ran our experiment. Another thing we discovered was larger targets make for louder impacts. It also might be easier to bring a small digital voice recorder to the range instead of a laptop, and do the math at a later time. We did show that by through a simple recording technique, it is possible to find the speed of bullets at short and long distances. References Excel Spreadsheet of above calculations Audacity Wikipedia Mesowest

100 Days of Sacramento MLS Housing Stats

Now that summer is over, I thought I'd post some housing inventory data I've been gathering. The Sacramento Bee is kind enough to give access to MLS records through their web site (click for a larger image):

Since I started gathering data on June 22, inventory has increased by over 2400 homes, or by 33%. Some interesting features of the data set include the weekly listing peaks every Saturday, and the end of the month decreases when homes that don't sell are automatically dropped from the MLS. According to this article, prices in Sacramento in August continue to show year-over-year increases, although monthly appreciation has moderated. There were 3806 resale home transactions that month, while MLS inventory increased by 1071. That means that 20% of all newly listed homes didn't sell. Inventory seems to be leveling off near it's peak, but this could just be the usual end-of-the-month dropoff. It will be interesting to see what happens with inventory this Fall. Traditionally, Fall is a slow period for real-estate. If inventory continues to build, we could be looking at price corrections at some point.

Robert Shiller Studies

Came across these interesting studies done by none other than Robert J. Shiller of Irrational Exuberance fame and his partner Karl E. Case: http://www.cswv.com/research/homeprice/ Some interesting "myth busting". While studying the economics of the late '80s busts in Boston and Los Angeles, they discovered that high unemployment was a trailing indicator of the recession, and that real-estate prices began falling before employment figures dropped: "The fact that prices have since collapsed in both Boston and Los Angeles adds weight to the argument that part of the explanation for the booms lies outside the fundamentals. It is true that the fundamentals deteriorated after 1988 in both cities. This can be seen in Table 5. Employment declines in Massachusetts began in 1989 and became severe in 1990 and 1991. Serious employment decline began in California two years later. But notice that the economic fundamentals deteriorated after the housing market had turned, not before. Case (1991) presents evidence that the economy of Massachusetts was driven on the way up and on the way down by the real estate cycle itself, not vice versa." What they mean by "fundamentals" are the normal factors that drive housing appreciation, like income and jobs. One way they define a real-estate bubble is when prices rise above what "fundamentals" would dictate, or when employment figures skew in favor of job types that are directly or indirectly related to servicing the bubble. For instance, I recently graphed some data I pulled from the California Department of Real Estate:

As of February 2005, there are currently over 303,000 licensed real-estate sales agents in California. That's a 60% increase since August of 1998! Competition is fierce out there. The California Association of Realtors reports a record of over 601,800 existing home sales in 2004. That’s less than two per agent! For the average agent selling the average number of homes at the average price ($450,000) for the average commission (1.5%), the annual gross was a paltry $13,500 in 2004. However, multiplying the number of homes sold (602,000), times the median price minus a fudge factor ($400,000), times the total commission paid per transaction (6%), the amount of money paid in commission by Californians last year was over $14 billion dollars! No wonder I see so many Hummers out there!

Home and Fincance News

As you all must know by now, I read a lot of news. I mean a lot of news. Probably way too much news. It's just that there's so much news online these days, and I'm a fast reader... Anyway, it seems like real-estate is on everybody’s mind these days. I've stopped bringing the subject up because I thought people were sick of it, but I was wrong. Maybe you guys just like I hear me rant (for some reason), so you throw a topic at me so you can watch the fireworks. Are you that desperate for entertainment? Isn't The Office funny enough for you? Good god! Anyway, Jason sent me a home finance link yesterday, with this flippant remark:

Why isn't this on your blog?

As if you don't already have a home?? As if these kinds of problems are in your distant past?? As if my sister isn't already canceling social events in favor of stripping wallpaper and choosing new custom frames for your cool new Irish artwork?? Give me a break! Well, for your information, I have a ton of new home finance links for you to read and ponder: L.A. Times: Middle Class investors are buying property instead of stocks for their retirement N.Y. Times: The real-estate market feels more like the dot-com market in 1999 Wall Street Journal: Institutional investors are selling real-estate holdings as fast as they can MSNBC: Sellers are having a harder time in other (not California) parts of the country L.A. Times: People are finding it hard to move to California Detroit Free Press: More people use stated income loans to buy property USAToday: More people use adjustable rate mortgages AFP: More bubble debate USAToday: People with adjustable-rate loans are going to suffer L.A. Times: People with interest-only loans are going to suffer L.A. Times: Title insurers have been stealing from home buyers So there you have it. Back by popular demand. Two weeks of home-buying-related junk. Maybe I should do another natural disaster entry? This real-estate stuff is way too depressing...

Economic Pessimism

Since my last post, the economic pessimists have become much more shrill. The problem is, I find it hard to disagree. Even the Federal Reserve is admitting that ultra-low interest rates are creating market distortions. The situation is exacerbated by Asia's insatiable appetite for U.S. Treasury Bills. According to the articles below, these low rates have created three kinds of problems for the world economy:
-Inflation of both assets and commodities that lead to greater risk taking and higher debt loads
-Low savings rates in the U.S., and too much saving in Asia
-Huge trade imbalances that lead to overcapacity in Asia and undercapacity in the U.S.
In other words, the cheaper money is, the more people will borrow. The more money they have, the more they will "invest" in ever inflating assets because there's no interest-rate benefit to saving. Problems arise when people overborrow on inflated assets to support short-term spending, or when they carry large debt loads on inflated assets they might need to sell in the near future for whatever reason (retirement, for example.)
Right now, people in the U.S. are spending like there's no tomorrow. In fact, people are increasing their spending 50% faster than their income is growing.!!
It will be interesting to see how this all turns out. In the meantime, I don't feel a pressing need to rush into this inflated housing market. Since I can't compete with those who are willing to spend 50% or more of their monthly income on a house payment anyway, I'll continue to save and hold tight until sanity returns.
Recent Articles of Interest
The percentage of first-time buyers hits a record low in area.
Game Over
Bond bubble, American-style
China's Exports Rise 33%; Trade Gap Widens to Record
Call for Adjustable Mortgages Jumps
Foreclosures grow as refinancing increases
World On Brink Of Ruin
Sites of Interest
Professor Piggington's Econo-Almanac
The Daily Reckoning