Metric Conversions Ws: Fill & Download for Free

The conversion between wet-bulb and dry-bulb temperatures is surprisingly non-trivial. Full details can be found in Chapter 6 of the ASHRAE Fundamentals handbook. (My notation differs slightly from ASHRAE's.)To convert between the two, you need to know either the dry-bulb or the wet-bulb temperature, in addition to atmospheric pressure and relative humidity. In metric units, the calculation goes as follows. First, absolute temperature ([math]T[/math], in Kelvin) is related to the Celsius scale ([math]t[/math]) as[math]T=t+273.15.[/math]You can compute the saturation water pressure for a given absolute temperature:[math] \ln p_{\rm ws}(T)=\sum_{i=-1}^4C_iT^i + C_l\ln T,[/math]where the coefficients have different values for [math]t<0~^\circ{\rm C}[/math] and [math]t>0~^\circ{\rm C}[/math] (i.e., below and above freezing). For the former,[math]C_{-1}=-5.800 220 6\times 10^3,[/math][math]C_0=1.391 499 3,[/math][math]C_1=-4.864 023 9\times 10^{-2},[/math][math]C_2=4.176 476 8\times 10^{-5},[/math][math]C_3=-1.445 209 3\times 10^{-8},[/math][math]C_4=0,[/math][math]C_l=6.545 967 3,[/math]whereas for the latter (above freezing),[math]C_{-1}=-5.674 535 9\times 10^{-3},[/math][math]C_0=6.392 524 7,[/math][math]C_1=-9.677 843 0\times 10^{-3},[/math][math]C_2=6.221 570 1\times 10^{-7},[/math][math]C_3=2.074 782 5\times 10^{-9},[/math][math]C_4=-9.484 024 0\times 10^{-13},[/math][math]C_l=4.163 501 9.[/math]From [math]p_{\rm [/math][math]ws[/math][math]}[/math] and the pressure [math]p[/math], the humidity ratio at saturation can be calculated:[math]W_s(T,p)=0.62198\frac{p_{\rm ws}(T)}{p-p_{\rm ws}(T)}.[/math]Given a relative humidity [math]\phi[/math] at dry-bulb temperature [math]T_{\rm db}[/math], the water vapor pressure is given by[math]p_w(T_{\rm db},\phi)=\phi p_{\rm ws}(T_{\rm db}),[/math]and if the pressure and water vapor pressure are known, the humidity ratio can be calculated as[math]W(T_{\rm db},p,\phi)=0.62198\frac{p_w(T_{\rm db},\phi)}{p-p_w(T_{\rm db},\phi)}.[/math]Finally, the relationship between dry-bulb and wet-bulb temperature is given implicitly by the following equations. First, above freezing:and below freezing:These equations can be solved numerically to obtain the desired temperature from the other temperature value if [math]p[/math] and [math]\phi[/math] are also known. There is no closed form solution.

Let's see what the savings are:A mid-sized airliner carries maybe 20% of its mass in fuel. This fuel has an energy density of 43 MJ per kg. Of that chemical energy at most 40% is converted into useable work. Heck, let's make this 25% so we are really conservative. Thus, the energy for the whole trip is, relative to the aircraft mass:Now assume that this airliner saves the energy to accelerate from 0 to 150 knots by using a catapult. This energy isSince I picked metric units, conversion is easy: 1 J = 1 Ws = 1 kg⋅m²/s². I use “mass” for the take-off mass instead of the usual “m” so you don't think it is the unit meter. Now let's put that into proportion:Using the catapult saves 0.1385% of the energy needed to fly a typical airliner trip, assuming the same efficiencies during acceleration as during the flight. Granted, it is more for short-range flights, but still insignificant to what is needed to move the aircraft 10 km up into the sky and then for a couple of hundred miles through the air at Mach 0.8. Still, let’s even double that proportion to 0.277%. In terms of fuel mass, these 0.277% are taken from 20% of the take-off mass. So the fuel needed to accelerate to take-off speed is 0,0554% of the whole aircraft take-off mass.To make a catapult launch feasible, you need to add some strength to the nose gear and the forward fuselage. The typical landing gear fraction of the take-off mass is about 3%, and the nose gear is 10% - 15% of that, so the nosegear mass is 0.375% of total mass. Relative to the nose gear mass, the fuel saving from using a catapult launch is 15% of the nose gear mass. Thus, the reinforcements need to add less than 15% to the mass of the nose gear.If we assume an acceleration of ½ g = 4.903 m/s², the take-off run to accelerate to 150 kts is 607 m. I expect that even this moderate acceleration (which requires a pulling force of half of the lift at take-off) would translate into much higher mass increases than those 15% of the nose gear mass.

The answer is certainly colored by your location and fandom. So for full disclosure, Bay Area, Giants, Warriors, 49ers, Sharks, Michigan Wolverines. Also, it depends on the which sports are currently playing but enough with the caveats now to the rankings.Bud Geracie - Ok this is a joke. Bud is not part of The Athletic but In the Wake of the Week was that good.Anthony Slater - It is Warriors season right now so this is clearly coloring my view but the 5 observations after every Ws game is just mandatory reading.Andrew Baggarly - I have read Baggs for years and was very excited when he joined the squad. Also, the 162 of baseball makes Baggs seem like part of my family. His writing style is a blend of sports poetry and information that is right in my wheel house.Ted Nguyen - His break down of film makes me smarter about the NFL. It is impossible to not learn something from every article.Eno Sarris - Same as Nguyen but with less film and more advanced metrics.Dane Brugler - College football scouting and ratings is like catnip to me.Danny Leroux - The fact the Danny is #7 shows how strong the stable is. I genuinely get excited when I see an article of his in my feed.Jon Middlekauff - The former scout point of view. I love the learning about the inner workings of front offices.Ethan Strauss - More of a national guy instead of just Warriors but when those two worlds collide I save the story until nobody will interrupt me.Melissa Lockard - I’m not even an A’s fan but her coverage of the A’s farm system makes me jealous (both of the prospects and the writing) as a Giants fan every time.Matt Barrows - I think this just shows how bad the 49ers are right now that Matty is this low. But hey there is always the #2 pick and next year, right?Corey Pronman - Prospect ranking is my vice and Corey loves Ryan Merkley (volatile and talented 1st round pick of the Sharks) so I am heavily invested.Jayson Stark - If you are a baseball fan and don’t read Jayson Stark, you aren’t actually a baseball fan. Nuff said.Ken Rosenthal - I hate to copy and paste but…If you are a baseball fan and don’t read Ken Rosenthal, you aren’t actually a baseball fan. Nuff said.Kevin Kurz - The only Sharks info I get is colored through Kurz colored glasses. Sharks 2019, cup or bust and hopefully it is cup.Ken Pomeroy - Come NCAA tourney time Pomeroy rockets up this list.Cody Stavenhagen - Good supplemental info to Home | mgoblog but need more to be primary.Tim Kawakami - Is the Godfather of The Athletic Bay Area and just doesn’t have the time to crank out as many articles. But when he does it is gold. Warriors in the arena — where and how Silicon Valley... and so far this Warriors/Silicon Valley is the most conversation inducing article of 2019.Marcus Thompson II - Sorry Marcus. I love the podcast banter especially with Kawakami but I just love the statistical angle more than the relationship one.Steve Berman - I had no idea I wanted to know amount the Bay Area media market. But I read every one of those articles.This really is a murders’ row of sports writing. Reading the journalists above flat out makes me a smarter fan. Keep up all the good work.