Monday 1 December 2014

Golf Club Trajectory

What Is the Loft of a golf club?

Loft angles are expressed in degrees with respect to vertical rather than the ground. The more highly lofted a club is, the higher the golf ball will go on impact. The below diagram represents the loft angle of a club blade and the trajectory angle it has.

                                                                                   



























So what are the official loft angle for each golf club?


There aren't any official values. Manufacturers are allowed to set the angles to whatever they wish. By slightly reducing the loft angle of a club, the ball travels farther. In this sport, distance sells. In the industry they call it creep when changing the loft angle for more distance. Below is a chart that shows the typical loft angles for a set of irons.



Club
Loft Degree
4 Iron
25
5 Iron
28
6 Iron
31
7 Iron
34
8 Iron
37
9 Iron
41
Pitching Wedge
45
Gap Wedge
50
Sand Wedge
55
Lob Wedge
60





Mean x (x̄): 5.5
Mean y (ȳ): 40.6
Intercept (a): 19.4
Slope (b): 3.8545454545455
Regression line equation: y=19.4+3.8545454545455x
*club 1= 4 iron, club 2=5 iron...ect

When looking at the graph, we can conclude that Club 1 (4 iron) has the smallest degree of loft and Club 10 (Lob wedge) has the largest degree of loft.



What are the official distances with each golf club?


Club
Distance (yards)
4 Iron
170
5 Iron                       
160
6 Iron
150
7 Iron
140
8 Iron
130
9 Iron
120
Pitching Wedge
105
Gap Wedge
90
Sand Wedge
70
Lob Wedge
40



Sample size: 10
Mean x (x̄): 5.5
Mean y (ȳ): 117.5
Intercept (a): 191.33333333333
Slope (b): -13.424242424242
Regression line equation: y=191.33333333333-13.424242424242x
*club 1= 4 iron, club 2= 5 iron...ect

From this graph we can conclude that Club 1 (4 iron) can hit the ball the farthest out of all the clubs (approx 170 yards.) We can also confirm that Club 10 (Lob wedge) has the shortest range out of all the clubs (approx 40 yards.) When comparing this graph to the above one, we can get an idea of the club loft vs. its distance. For example, Club 1 (4 Iron), has the lowest possible loft degree of 25 but in return it can be used to deliver the longest distance of all the clubs. The 4 iron, when used, is able to hit the golf ball the farthest out of any irons. If we take a look at Club 10 (Lob wedge), it has the absolute highest degree of loft (60 degree) out of all the irons but the shortest distance (40 yards.) The lob wedge when used has the shortest range out of all the irons.

When trying to determine what club to use, it all depends on your yardage to the hole. If you have a far shot that is around; 170-200 yards then pick the 4 iron, if your only 100 yards away from the pin then the pitching wedge would applicable for this situation. If you would like to hit a longer shot, then a lower loft degree on the club face is needed. For a shorter shot, a higher degree of loft will need to be used to launch the ball high and controlled instead of long.

There are two regulations in golf club production, 1. Form and Make of clubs, and 2. Foreign Materials. These regulations are needed so that no club has the potential to out perform another club based on what it is made of. If a producer added some foreign materials in or on the club face, and a player was able to hit farther and more accurate, the player and the producer would then be investigated by the USGA (United States Golf Association.)



Dylan Pescod



Research:

http://www.leaderboard.com/loftinfo.htm
http://www.alcula.com/calculators/statistics/linear-regression/
http://www.usga.org/Rule-Books/Rules-on-Clubs-and-Balls/Rule-4-%E2%80%93-Clubs/




















Wednesday 26 November 2014

House Prices in Calgary Over Three Generations


    House Prices in Calgary
The Costs of Ownership Over 3 Generations


   Rising house prices in Canada have been a hot topic in the last few years. Talk of housing bubbles and highly competitive housing markets seem to make the news at least once a week, and Calgary has been said to have the fastest increasing housing prices in the country. None of this comes as a surprise to the 20 and 30 somethings living in the city and across Canada.  While the desire to buy that all important first home is still as strong as ever, the average age that people are able to make that jump is ever climbing. A recent CIBC study has shown that the average age to purchase a first home is now sitting at 29, and with fewer and fewer 25-35 year olds buying, that average is expected to rise. In an attempt to afford this milestone purchase, people are living with their parents longer and 30-40% are expecting their parents to assist them in the purchase of the all important first home. In fact, your odds in favor of living at home at age 30, is 42.3 : 57.7 while the odds in favor of owning a home is 50 : 50.  This is not an arrangement that many people in their teens or early 20's would hope for as they near 30, but between increasing student loan costs, lower entry level wages, increasing home prices and by extension growing down payment size many have no choice.

  Some people argue that lower interest rates and higher salaries have compensated for the increased housing costs and this new generation of home buyer are too lazy to work hard and entitled enough to simply expect everything handed to them. So, how much have home prices risen in the last generation and have salaries risen to match? Is the overall cost of living and home ownership really as unattainable as the media is touting or are today's low interest rates leveling the playing field? In terms of percentage of income spent on housing are home buyers of today paying more?  Let's take a fictitious family and follow them over 3 generations. The first of which buys a home in the same year as their child's birth in 1982. 29 years later, at the average age of first time home ownership, their son wishes to purchase a home in the same area. Will he be able to afford it? What about his daughter, 29 years later?

  First, we need to even out the value of money level by accounting for inflation and make everything equivalent to 2012 dollars. According to Statistics Canada the median income in Canada in 1983 was about $42 000. If you adjust for inflation that number becomes about $86 927. (Bank of Canada Consumer Price Index 2.54 averaged from 1983-2012. A=P(1+i)^n. A= 42000 (1+0.0254)^29. A= 86927.14) That is not all too different than the Alberta 2012 median income $94 460. In terms of spending power, today's median income earner has only $7533 more to spend annually or 8.7%. (94460-86927 = 7533 / 86927 = 0.08666) Projecting to the third generation, an 8.7% increase in salary would give the granddaughter $95 281.

  Taking a closer look at home prices in the Westgate area in South West Calgary using MLS and Calgary Real Estate Board we discover that the average home in the area is a 3 bedroom, 1 bathroom home of about 1 200 sq feet and built in the 1960's. The average sale price in 1983 was $85 869. Using the Consumer Price index to adjust for inflation to 2012 dollars the price is $177 723. ( A=P(1+i)^n. A = 85869 (1 + 0.0254)^29 = $177 723 ) In 2012, the average sale price $456 934. That's an increase of $279 212 or 157% over 29 years. (456935 - 177 723 = 279212 /177723 = 1.571 or 157%) A huge increase with less than 9% more income to compensate for the skyrocketing prices. If we graph the linear regression, we can estimate that is prices continue to rise in the same manner, the granddaughter will be paying about $746 116 for the same home. (9971.821428x +167751.17857143 then finding x=58) Charting the salaries and home price below we can see how fast prices are outpacing salary.



 The first step to buying a home is saving for the down payment. A 20% down payment allows the buyer to forgo mortgage insurance, so let's assume that is the number each generation is saving for. A $35 545 lump sum in 1983 (177723 x .2 = 35 544.6), $91 387 in 2012 (456934 x .2 = 91 386.8) and a whopping $149 223 in 2041(746117 x .2 =149223.4). We go from 40.8% to 96.7% to 156.6% of annual earnings just to get a down payment. It is clear to see that if things continue, owning a home will be beyond what the average family can afford in just one generation. This is not a matter of low work ethics or high expectations of a new generation, but the costs far outstripping what can reasonably be afforded.



  Our families are good savers and they managed to put away enough to jump into the market. What sort of monthly payment are they going to have? Assuming a 25 year mortgage and using the 1983's interest rate of about 10%, our grandparents will be paying $1292 a month or 17.8% of their monthly salary towards their mortgage. ($86927/12 = 7243.92. 1292/7243.92 = 0.178)  Their son in 2012 has the advantage of an interest rate of 5.14%, but their payment will be $2167 or 27.5% of their monthly income. (94460/12 = 7871.67.  2167/7871 = 0.275). In 2041, maintaining the 5.14 interest rates, the granddaughter will be paying out $3378 or 42.5% of her monthly pay. Experts suggest that your housing payments be no more than 25-29% of your monthly income, so even in 2012, the son is pushed to the limits of what is financially healthy, as things like taxes and insurance are not included in this price. His daughter is well over that threshold and without a second income, she could not afford to purchase a home.

Mortgage Payment as a Percentage of Monthly Income


   Even with low interest rates the families in 2012 are barely able to afford their home, which begs the question, what would happen if interest rates were to rise? With interest rates at a 50 year low, this is a distinct possibility. If rates were to go up to the same level as in the 80's, the son's payment would jump to over $3300, beyond what the son could take on and maintain that 25-29% of monthly earning that is suggested. So, the lower interest rates do help considerably, but the financial stretch on the "average family" is clear. This is to say nothing of the following generation, which already is unable to afford a home with the lower interst rates. If rates climb now, then many families will find they have to tighten their belts to make ends meet or be forced to sell and move to a more affordable neighborhoods. Westgate is beginning to be considered inner city, a title that seems to be linked to higher prices. It is no wonder that areas such as Cochrane and Okotoks are finding their populations increase, as families move further from the city core in search of affordable housing. Established neighborhoods such as Westgate also have a higher price tag compared to new neighborhoods. Perhaps it is no surprise that the demographics in Westgate show that about 50% of the residents are over 50 and 52% of homes are not owner occupied. It is simply financially out reach for many young people who are taking on longer commutes in order to own a house.

   It is clear that things cannot continue of the same path. The costs are fast outstripping pay and the pinch is already being felt. Without a correction in house prices, or an increase in salary we will be facing a market like in Europe, where home ownership is for the very wealthy, and the gap between rich and poor will continue to widen.


References 


Average income
http://www.conferenceboard.ca/hcp/hot-topics/caninequality.aspx
http://www.statcan.gc.ca/daily-quotidien/140130/t140130a001-eng.htm
http://www.theglobeandmail.com/news/politics/who-are-the-1-per-cent-a-snapshot-of-what-canadians-earn/article14269972/?page=all
http://www.statcan.gc.ca/tables-tableaux/sum-som/l01/cst01/famil108a-eng.htm

Calgary housing prices
http://www.calgaryherald.com/news/calgary/Calgary+resale+housing+price+growth+highest+Canada/10204823/story.html
www.MLS.ca

CIBC averages
http://homeownership.ca/homeownership/are-you-the-average-first-time-homebuyer-in-canada
Inflation
http://www.statcan.gc.ca/pub/11f0019m/2010325/part-partie1-eng.htm#h2_3

Interest rates
http://www.economics.gov.nl.ca/archives/E1989/List%20of%20Diagrams/Selected%20Canadian%20Interest%20Rates%201983%20to%201988.pdf
http://www.ratehub.ca/historical-mortgage-rates-widget

Living arrangements
http://www12.statcan.gc.ca/census-recensement/2011/as-sa/98-312-x/98-312-x2011003_3-eng.cfm

Mortgage calculator
http://www.zillow.com/mortgage-calculator/

Percentage of income for Mortgage
http://www.bankrate.com/finance/mortgages/how-much-house-can-you-buy--1.aspx