By: Michael Petesch
Competition
There are several ways to travel between countries across oceans, but commercial airliners currently have a monopoly on travel speed. Before the introduction of motorized ships, a reasonable transatlantic travel time for sailing ships was one to two months. Motorized ships running on coal brought a spectacular improvement in speed and reliability further reducing one-way transatlantic travel to 16 days in 1840.[1] With the advent of diesel engines and alternative, weight reducing building materials, travel times were decreased even further. In 1952, the SS United States built primarily out of aluminum set the record for the fastest transatlantic crossing of 3 days and 12 hours at a speed of more than 54 km/h which still stands today.[2]
Another form of transportation that appeared before and remained competitive with the commercial airliner until the 1940s and 50s were airships, specifically Zeppelins. Perhaps the most successful passenger airship of all time was the LZ 127 Graf Zeppelin. It logged over a million miles during its life -- including the first round-the-world flight in 1929. On October 11, 1928 it departed Friedrichshafen, Germany inaugurating aerial transatlantic passenger service. After a flight of 111 hours and 44 minutes, the ship landed at Lakehurst, New Jersey on October 15, 1928. It carried a crew of 40 members and 20 passengers[3] The return trip to Germany took 71 hours and 49 minutes, or just under three days. Ocean liners of the day took twice as long to carry passengers across the Atlantic.[3]
Despite faster travel times, zeppelins were severely disadvantaged in other ways. Passenger loads were normally if not always under 100 people and because of their enormous size they were very resource intensive requiring huge manufacturing hangers and specialty docking areas. The grand zeppelin era when out in a blaze as the infamous Hindenburg, buoyant with explosive hydrogen, became a gigantic floating then falling fireball.
Birth of International Flight
Advantages
Speed
As the ear of the zeppelin self-destructed, the public demand for quick travel edged other modes of transit as well. By the 1940s and 1950s, commercial transatlantic flights had ushered in a new reference system measured in hours rather than days. A single commercial airplane could travel from NYC to London across the Atlantic Ocean in 5 or 6 hours. Quickness and directness have been and continue to be the greatest assets of aviation. Most vacationers and travelers today are limited in travel time due to work obligations consequently increasing the importance of quick, hassle-free travel. Previously, with ships and zeppelins, travelers would have determine if the duration and quality of potential vacation experiences would outweigh the duration of travel time. Now, vacationers can book a plane ticket, hop a plane and have a meal in a country thousands of kilometers away in the same day.
Capacity
Passenger capacities also make airline travel very competitive. Early passenger loads were similar to those carried by Zeppelins, but with technological advances in building materials, weight saving techniques and increased engine thrust, hundreds of passengers can now be moved at once.
Safety
Safety is another advantage of airline travel. Based solely on deaths or even crashes per kilometer traveled, airplanes are one of the safest means of transit ever. Pilot expertise and safety regulations on planes have reduced the amount of flight accidents. Air travel generally avoids most weather patterns by flying above the clouds, which makes the trip safe and unaffected by storm activity. On the other hand, sea travel is directly affected by any weather changes, which create wind or cause large waves, sometimes extending the voyage making it tedious and more dangerous. Sea travel also requires skilled navigation to avoid dangerous rock formations or ice flows, while air travel has fewer such dangers.[4] These dangers can be further reduced by using auto pilot technology.
Pricing
Lastly, demand for air travel has increased the number of international flights and carriers, making commercial airliners even more desirable. Initially, flying was a very expensive mode of transportation, which only the wealthy could afford but as markets went global companies began paying for businessmen to fly. Now, competition between carriers has driven down flight costs and increased travel options with regards to varied flight times, directness, amenities and comfort.
Innovation
- Jet engine: Although patents for working gas-powered jet engines have been awarded since the late 1700s the first to actually power an airplane was developed by a German named Hans von Ohain. A successful first flight on August 27, 1939, established the Heinkel He 178 as the world's first jet plane.[5] By the 1950s the jet engine was almost universal in combat aircraft and was becoming common on British commercial passenger planes. By the 1960s, all large civilian planes were jet powered despite piston and prop engines being more efficient fuel burners. With the advent of high bypass turbofan jet engines which better performed at high speeds and high altitudes, jet engines became as efficient as precursor engines.[6] Additionally, gas turbine engines phased out props in commercial applications because they have a great power-to-weight ratio. Gas turbine engines are also smaller than their reciprocating counterparts of the same power. Consequently, commercial airliners were encouraged to grow.
- Kerosene fuel: Increases in flight altitudes and lengths meant components and fuel would be subject to a greater number of conditions. Jet fuel known as Jet-A was developed especially for commercial jet planes provided much needed consistency and reliability. Jet-A is pure kerosene which has a high flashpoint (temperature at which fumes can be ignited by an open flame) and is high in octane (ensures efficient fuel burning). It is often mixed with antifreeze to prevent ice build up in the fuel tanks, potentially blocking fuel lines and stalling engines.
- Auto pilot: Navigational accuracy is an essential part of an auto pilot system. By reducing minute navigational errors commonly made by human pilots, auto pilots can reduce flight times and maximize fuel efficiency. As a result, auto pilot systems ensure reliable maximum linear distances.
- Composite Materials: Since the use of aluminum for airplanes in the 1920s, several composite materials combining two or more organic or inorganic components such as fiberglass, carbon fiber, and other exotic fibers have been developed and used. The greatest value of composite materials is that they can be both lightweight and strong. The heavier an aircraft weighs, the more fuel it burns, so reducing weight is important to aeronautical engineers.[7] On the other hand, aluminum can be repaired after sustained denting. Composites cannot. Although about 10% of the structural weight of the Boeing 777 is composite material, commercial airliners will likely continue to be built using aluminum because it requires less maintenance.[7]
Policies
- Fuel types were regulated to ensure safety. Jet engines are much more sensitive to the chemical and physical properties of fuel than gasoline and diesel engines.[8] "Advances in engine and aircraft design greatly expanded varieties of flight envelope which necessitated new standards for turbine engine fuel quality. This led to the introduction of a variety of fuel types for different purposes and to the development of specifications to ensure the fuel met equipment requirements and burned reliably under all flight conditions."[8]
- Runway length: Each plane model has minimum takeoff and landing distance requirements. Runway lengths had to be standardized not only to to make international flight possible but to encourage it.
Growth Period
Policies
- Runway Protection Zones: "Trapezoidal areas off the end of the runway end that serve to enhance the protection of people and property on the ground in the event an aircraft lands or crashes beyond the runway end."[9] Airports must adhere to three stipulations under FAA design criteria with regards to RPZs. First, the airport must own the land. Second, the airport owner must protect the RPZ from both obstructions and incompatible land uses. Finally, the airport owner must strive to attain compatible zoning around the airport in order to prevent incompatible land uses that could cause or lead to conflicts that endanger the airport, cause the airport to close, to require substantial remedial investment to purchase conflicting developing property.[9]
- Landing Fees: A regulation that requires a an airplane pay a fee to the airport at which it lands. If lots of planes want to land at a busy airport, the landing fees will be high due to great demand for a fixed amount of terminals. These high costs disproportionately favor large commercial airplanes because they can carry large numbers of people to offset the costs of the fees. Therefore, high landing costs encourage larger planes.
- Runway Length: As commercial planes become bigger and bigger they require more and more runway to takeoff and land on. As a result, airports often have to extend their runways in order to capture the business of these larger airplanes. By actively protecting RPZs early on airports can accommodate runway extensions and reap the benefits the larger airplanes bring.
- Security Procedures: Many of the security policies such as full body scans, liquid restrictions, shoe and belt removal put in place after 9/11/01 have made international travel more bothersome than it used to be. The outcomes of one day ten years ago has and will continue to negatively impact the growth of international air travel.
Methodology
The process of calculating passenger kilometers involved several steps. First, an "international flight" was defined as a flight consisting of at least 5568 km (the distance from NYC to London). This established the minimum flight range and eliminated commercial passenger planes flying prior to 1938. It also insured consistency throughout the data and subsequent analysis. Secondly, a list of planes and their first service years was put together with the help of Wikipedia. Thirdly, aircraft technical data and specifications regarding the maximum passenger configurations of each plane, their maximum flight ranges, and entry date into service were obtained.[10] Fourthly, passenger kilometers were calculated as the product of the number of passengers a plane can carry multiplied by that planes flight range.
Table 1: Data for Past, Present and Future Passenger KM
| Plane Model | Year | Passengers | Range | Passenger KM | Predicted Passenger KM |
|---|---|---|---|---|---|
| Boeing 314 | 1938 | 77 | 5633 | 433718 | 702543 |
| Boeing 377 | 1947 | 114 | 6759 | 770554 | 986467 |
| Brabazon | 1949 | 100 | 8047 | 804672 | 1063177 |
| Boeing 707-120 | 1957 | 179 | 8704 | 1558088 | 1430951 |
| Boeing 707-320 | 1958 | 189 | 6917 | 1307355 | 1484619 |
| McDonnell DC-8-63 | 1959 | 259 | 7232 | 1873104 | 1540179 |
| Tupolev Tu-114 | 1961 | 224 | 10944 | 2451353 | 1657203 |
| McDonnell DC-8-61 | 1965 | 269 | 8945 | 2406248 | 1916546 |
| Boeing 747-100 | 1970 | 452 | 8575 | 3875792 | 2293297 |
| McDonnell DC-10 | 1971 | 380 | 10001 | 3800304 | 2376301 |
| Airbus A330 | 1974 | 300 | 7686 | 2305740 | 2641808 |
| Concorde | 1976 | 144 | 6232 | 897405 | 2833221 |
| Boeing 747-300 | 1983 | 496 | 12168 | 6035149 | 3602112 |
| Boeing 747-400 | 1989 | 524 | 13446 | 7045452 | 4395359 |
| McDonnell MD-11CF | 1990 | 410 | 12168 | 5186156 | 4540464 |
| Airbus A340-300 | 1993 | 295 | 13242 | 3906331 | 4998688 |
| Boeing 777-300 | 1998 | 550 | 11019 | 6060670 | 5840251 |
| Boeing 747-400ER | 2002 | 524 | 14205 | 7443336 | 6584145 |
| Airbus A340-500 | 2004 | 313 | 16048 | 5022893 | 6979355 |
| Airbus A380 | 2005 | 840 | 14816 | 12445440 | 7182659 |
| Boeing 787-8 | 2010 | 250 | 15742 | 3935500 | 8253967 |
| Boeing 747-8 | 2011 | 450 | 14816 | 6667200 | 8478677 |
Table 2: Regression Statistics for Predicted Model
| K Value | 27000000 |
| Multiple R | 0.8553 |
| R Square | 0.7315 |
| Adjusted R Square | 0.7181 |
| Standard Error | 0.5326 |
| Observations | 22 |
Table 3: ANOVA Statistics for Predicted Model
| df | SS | MS | F Score | Significance F | |
| Regression | 1 | 15.4541 | 15.4541 | 54.4827 | 3.95E-07 |
| Residual | 20 | 5.6730 | 0.2837 | ||
| Total | 21 | 21.1272 | |||
Table 4: Statistical Results for Predicted Model
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | -79.0493 | 10.4288 | -7.5799 | 2.65478E-07 | -100.8034 | -57.2952 |
| X Variable 1 | 0.0389 | 0.0053 | 7.3812 | 3.95048E-07 | 0.0279 | 0.0499 |
Using the regression tool in excel, regression results for several K values ranging from 17000000 to 31000000 were produced. Then the adjusted R squared, F score and T score from each result of K were placed in a table and visually compared (refer to table 6).
Table 6: Statistical Comparison Table
| K value | Adjusted R Square | F Score | T Score |
| 17000000 | 0.702479572 | 50.58338869 | 7.11219999 |
| 18000000 | 0.706651792 | 51.58727892 | 7.182428484 |
| 19000000 | 0.709590042 | 52.31156993 | 7.232673774 |
| 20000000 | 0.711744049 | 52.85192183 | 7.269932725 |
| 21000000 | 0.713372065 | 53.26571282 | 7.298336305 |
| 22000000 | 0.714632535 | 53.58932794 | 7.320473205 |
| 23000000 | 0.715627717 | 53.8468594 | 7.338041932 |
| 24000000 | 0.716426308 | 54.05482449 | 7.352198616 |
| 25000000 | 0.717075988 | 54.22487715 | 7.363754284 |
| 26000000 | 0.717610766 | 54.36544126 | 7.37329243 |
| 27000000 | 0.71805546 | 54.48273329 | 7.381241988 |
| 28000000 | 0.718428545 | 54.58142382 | 7.387924189 |
| 29000000 | 0.718744015 | 54.66507769 | 7.393583549 |
| 30000000 | 0.719012625 | 54.7364539 | 7.398408876 |
| 31000000 | 0.719242758 | 54.7977145 | 7.402547839 |
As the values of K increased, the Adjusted R Square plateaued at about 71 percent indicating 71 percent of the movements (generated numbers) are explained in the adjustments of the variable. Additionally, the F score stabilized at 54 and the T score at 7.4 indicating that the model on the whole is statistically significant.
The Adjusted R Square value of .71 was associated with a K value of 27000000 km. After 27000000 km, all three measurements (adjusted R, F score, and T score) changed less than .1 between each subsequent K value. This minimal change indicates that all values of K after 270000000km are equally good models for determining K, even 50000000 km. Therefore, K = 27000000 was used as the best fit line of regression.
Table 5: S-curve Model Parameters
S(t) = K/[1+exp(-b(t-t0)]
| K value | 27000000 |
| Intercept | -79.0493 |
| b | 0.0389 |
| t0 = intercept/-B | 2031.0763 |
As previously explained, the K value of 27000000 was chosen because it marked the beginning of the plateau. Table 5 synthesizes the information gathered from the regression calculation for the K value of 27000000. Using the calculated intercept and b coefficient, t0 (the inflection point in years where passenger km begins increasing at a decreasing rate) can be figured. t0 for K = 27000000 is the year 2031. Using these variables, an S-curve was calculated using the equation S(t) = K/[1+exp(-b(t-t0)]. The resulting S-curve on the right depicts advances in passenger kilometers will begin to decrease after year 2031, and begin leveling off at 27000000 passenger kilometers in roughly the year 2170 in the graph. Because all parameters are maximum numbers, the determined inflection point is a relative extreme value if fuel types remain consistent. Changes in fuel type and fuel efficiency were not factored into this analysis.
Maturity
Policies
- Runway and terminal lengths will likely limit the final size of large planes. Although larger planes will continue to be more profitable than small planes in the presence of landing fees, terminal size will become an issue. A trade off will have to be made between the number of planes allowed to dock at an airport or the size of the airplanes allowed to dock.
- Some airports have more room to expand than do others. This may lead to a size specialization in commercial flight in which super mega planes are able to take off and land at select airports. However, this specialization is likely disadvantageous since in order to truly reap the benefits of a super mega sized plane it should be operated around the clock all year long. Not doing so, would be a waste of capital investment. Then again if super mega planes can only travel between select airports the number of trip options and possibilities go down further decreasing their economic viability.
Despite the model, the range of commercial airplanes has likely reached its peak because there is no need for a plane that can fly more than half way around the world. Therefore, to increase passenger kilometers per flight, planes will have to get bigger and carry more passengers. The Airbus A380 is currently the largest airplane in the world and like the Boeing 747 before it, will likely hold that title for several decades. Reason being, the costs of building larger planes and the costs of adapting infrastructure (terminals and runways) to accommodate larger planes will likely curb the growth in passenger kilometers per flight. Therefore, although the model predicts growth until year 2170, the growth will likely be sporadic and may result in a maturity plateau before 2170.
Conclusion
Demand for quick, safe and cheap international travel has driven airline companies to invest in larger airplanes, light weight composite materials and larger, more efficient engines. When combined, those factors have increased fuel burning efficiencies, and contributed to an increase in potential passenger kilometers per flight. Based on the maximum passenger capacity and flight range of 22 planes, passenger kilometers traveled per flight will exponentially increase until year 2031 then exponentially decrease until the technology plateaus around year 2170 according to the produced model. Although the model predicts this, it may be skewed by the enormous passenger capacity of the recently inaugurated Airbus A380. Introductions of mega planes such as the A380 are few and far between resulting in a rather sporadic data set which affects the inflection point and year of maturity. Additionally, other constraints such as the size of the world and length of runways have already begun to limit necessary maximum flight ranges and plane size (directly affects passenger capacity). Therefore, maturation of passenger kilometers per flight will likely happen earlier than the model predicts.
References
- ↑ Decker, Kris D. Life without Airplanes: from London to New York in 3 days and 12 hours. Low-tech Magazine. 4 June 2008. Retrieved 12 October 2011.
- ↑ Liner Transatlantic Crossing Times, 1838 - 1952 (in days). The Geography of Transport Systems. Retrieved 10 October 2011.
- 1 2 Graf Zeppelin History. Airships: The Hindenburg and other Zeppelins. 2009. Retrieved 12 October 2011.
- ↑ McKenzie, Richard B. Making Sense of the Airline Safety Debate. Cato Review of Business & Government. 1991. Retrieved 12 October 2011.
- ↑ Warsitz, Lutz: THE FIRST JET PILOT - The Story of German Test Pilot Erich Warsitz (p. 125), Pen and Sword Books Ltd., England, 2009
- ↑ Chapter 10: Technology of the Airplane. Quest for Performance: The Evolution of Modern Aircraft. Part II: The Jet Age. Hq.nasa.gov. Retrieved 12 October 2011.
- 1 2 Composites and Advanced Materials. US Centennial of Flight Commission.
- 1 2 The History of Jet Fuel. Air BP.
- 1 2 Runway Protection Zones. Central Region Airports Division. AIP Sponsor Guide – 500. 1 October 2010. Retrieved 14 October 2011.
- ↑ Aircraft Technical Data & Specifications. 2011. Retrieved 10 October 2011.