Odds and Ends, Archive 5
Santa Imposter Huge GHG Source
FORT COLLINS (SSPI) – A special SSE investigation has revealed a heretofore unrecognized source of carbon dioxide (CO2) accounts for over 3.6% of the anthropogenic greenhouse gases (GHG) emitted to the atmosphere every year. On a CO2-equivalent basis, over a billion metric tons of the global-warming chemicals are released every Christmas Eve as an unintended consequence of providing yuletide joy to billions of children world-wide. If this source were a country, it would rank sixth on a list of the highest emitters, about halfway between Japan and Germany.
During the 24-hour period beginning at sunset on December 24, the energy used in delivering toys to youngsters around the world creates 13 times the carbon footprint as all other sources on the planet combined for that day.
The SSE probe began months ago when sources close to North American Aerospace Defense Command (NORAD) told SSE investigators that the radar signature of “Santa Claus” abruptly changed in 1985. At that time NORAD scientists attributed the change to upgraded equipment, but since then additional information has been obtained through highly confidential channels that point to a much more nefarious development.
It appears that in February of 1985, while the reindeer and elves were soundly sleeping off the effects of the previous year’s finale, Santa Claus was overthrown in a military coup by his sinister and less talented cousin, Sandy Paws. Apparently Mr. Paws continues to masquerade as Cousin Santa to lull the population of the planet into a false sense of security until he feels safe in launching some dastardly plot – the nature of which SSE has yet to ascertain.
In the meantime, SSE has quantified the global-warming impacts of Mr. Paws’ Christmas Eve shenanigans using cold hard chemistry and physics, data acquired through trusted sources, reasonable engineering assumptions, and a few less reasonable estimates (guesses).
Here's What We Know
There were 6,706,993,152 people on the planet (last Christmas Eve’s data), 22.5% of which were children under the age of 13. Of course not everyone celebrates Christmas, but in the spirit of inclusion Mr. Paws continues Santa’s tradition of bringing a gift to each child under the age of 13, regardless of faith. The average weight of each toy is about the same as that of a Tonka Toughest Mighty Truck or about 7.95 lbs.
Mr. Paws had to replace all of Santa’s magically-endowed equipment with more pragmatic devices operable by mere mortals. Magic reindeer are replaced by reindeer-like avatars powered by turbine jet engines fueled by compressed natural gas (CNG) with a composition of 85% methane and 15% ethane. The engines have a thermal efficiency of 26.8% (our Nunavut-based agents obtained a manufacturer’s data sheet). Mr. Paws also designed the fuel systems to by-pass directly to the atmosphere 6 SCF of uncombusted fuel gas per reindeer-mile (Only eight reindeer here – Rudolf is a Gene Autry generated myth and not part of the real Santa’s menagerie.) The devious villain correctly predicted NORAD would pick up the IR scan of the methane and attribute it to the normal ruminant emissions of real reindeer.
The Sandy/Sleigh/Reindeer (SSR) vehicle has an empty weight of 30 tons (short) and a dimensionless drag coefficient of 1.13. The SSR vehicle possesses an aerodynamic reference area (for calculating drag forces) of 57,600 ft2 fully loaded and 400 ft2 when empty.
As you might expect, Sandy’s route is dictated by time zones – Asia first (with 60.4% of the world’s population), Australia/Oceania second (0.5%), followed by Africa (14.5%), Europe (10.9%), South America (8.6%), with North America (5.1%) last. (For children living in Antarctica, the toys are left with Fr. Jorge Diego at the Cabo de Hornos Jiffy Lube and Jerky Outlet in Tierra del Fuego, Chile.)
For ‘continent-to-continent’ travel, the average distance is 8,000 miles, cruising at 550 mph and 35,000 feet where atmospheric conditions average -50F and 3.47 psia. On each continent, Sandy makes an average of 250 ‘hub-to-hub’ connections traveling 850 miles on each connection at 450 mph and an elevation of 20,000 feet. The average conditions at that elevation are -20F and 6.76 psia. Out of each ‘hub’ location, Sandy makes an average of 75 local flights where the toys are dropped off for ground delivery by PawsEx agents. Each local flight averages 200 miles at 250 mph and an elevation of 5,000 feet where the temperature averages 48F and the atmospheric pressure is 12.23 psia.
Basis of GHG Emissions Estimate
To estimate Sandy Paws’ Christmas Eve carbon footprint, SSE technical experts made use of the above information as well as the following equations and assumptions to estimate the total energy required, the fuel used, and ultimately the carbon footprint. The total energy required is estimated to be the sum of the following three factors:
1.) Energy necessary to change the potential energy (elevation) of the SSR vehicle and its payload for each takeoff (assuming the average elevation at liftoff is 500 feet), using the equation:
ΔU = mgΔElev; where ΔU = change in potential energy, m = mass, g = gravitational acceleration, ΔElev = change in elevation.
2.) Energy necessary to change the kinetic energy (velocity) of the SSR vehicle and its payload for each takeoff using the equation:
ΔKE = 0.5m(vf^2 - vo^2); where ΔK = change in kinetic energy, m = mass, vf = final velocity, vo = initial velocity.
3.) Energy required to overcome drag forces using the equations:
FD = 0.5ρv^2(CD)(Ar) and W = F x d (Work done (energy required) = Force x distance). FD = Drag force, ρ = fluid density, v = velocity, relative to fluid, CD = dimensionless coefficient of drag, and Ar = aerodynamic reference area.
Unlike a helicopter which needs to expend energy to maintain altitude, the SSR vehicle appears to have wing-like structures providing the lift necessary to maintain altitude. Therefore the energy required to stay aloft is accounted for by the equations calculating the drag force.
The Mass Problem
The total mass of SSR vehicle is constantly changing – fuel is burned, toys are unloaded, the vehicle is refueled – so rigorous solutions of the energy equations would require calculus. We don’t do calculus unless threatened with confiscation of our pocket protectors. Instead we’ve estimated the energy required by calculating the initial payload for each intercontinental trip and using the average payload values for all the trips within each continent. Payloads are proportional to the number of toys left to deliver based on the given demographics.
The Fuel Problem
Since total mass is important in determining the energy required in both the potential and kinetic energy equations, it became clear to the SSE staff that some assumptions (this is where the ‘guesses’ come into play) would need to be made about refueling frequencies. Since little is known about Sandy Paws’ world-wide infrastructure and supply chain contacts, we made the simplifying assumption that the weight of the fuel on board would reflect the fuel/gross weight ratio of a fully loaded Boeing 747. So in calculating the weight of the fuel, we assumed that the weight of the fuel was equal to 35% of the payload + empty vehicle weight on any given leg of his journey.
There you have it, folks – all the information you need to calculate Sandy Paws’ carbon footprint. Clicking the ICON below will take you to a table summary of the relevant data described above.
If you try solving this problem independently – I’d love to compare results,, and therapists. If, on the other hand, you’d just like to find all my errors,, continue by clicking – HERE.
