National Academies Press: OpenBook
« Previous: Chapter 2 - Need
Page 18
Suggested Citation:"Chapter 3 - Demand." National Academies of Sciences, Engineering, and Medicine. 2013. Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook. Washington, DC: The National Academies Press. doi: 10.17226/22619.
×
Page 18
Page 19
Suggested Citation:"Chapter 3 - Demand." National Academies of Sciences, Engineering, and Medicine. 2013. Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook. Washington, DC: The National Academies Press. doi: 10.17226/22619.
×
Page 19
Page 20
Suggested Citation:"Chapter 3 - Demand." National Academies of Sciences, Engineering, and Medicine. 2013. Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook. Washington, DC: The National Academies Press. doi: 10.17226/22619.
×
Page 20
Page 21
Suggested Citation:"Chapter 3 - Demand." National Academies of Sciences, Engineering, and Medicine. 2013. Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook. Washington, DC: The National Academies Press. doi: 10.17226/22619.
×
Page 21
Page 22
Suggested Citation:"Chapter 3 - Demand." National Academies of Sciences, Engineering, and Medicine. 2013. Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook. Washington, DC: The National Academies Press. doi: 10.17226/22619.
×
Page 22
Page 23
Suggested Citation:"Chapter 3 - Demand." National Academies of Sciences, Engineering, and Medicine. 2013. Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook. Washington, DC: The National Academies Press. doi: 10.17226/22619.
×
Page 23
Page 24
Suggested Citation:"Chapter 3 - Demand." National Academies of Sciences, Engineering, and Medicine. 2013. Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook. Washington, DC: The National Academies Press. doi: 10.17226/22619.
×
Page 24
Page 25
Suggested Citation:"Chapter 3 - Demand." National Academies of Sciences, Engineering, and Medicine. 2013. Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook. Washington, DC: The National Academies Press. doi: 10.17226/22619.
×
Page 25
Page 26
Suggested Citation:"Chapter 3 - Demand." National Academies of Sciences, Engineering, and Medicine. 2013. Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook. Washington, DC: The National Academies Press. doi: 10.17226/22619.
×
Page 26
Page 27
Suggested Citation:"Chapter 3 - Demand." National Academies of Sciences, Engineering, and Medicine. 2013. Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook. Washington, DC: The National Academies Press. doi: 10.17226/22619.
×
Page 27
Page 28
Suggested Citation:"Chapter 3 - Demand." National Academies of Sciences, Engineering, and Medicine. 2013. Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook. Washington, DC: The National Academies Press. doi: 10.17226/22619.
×
Page 28
Page 29
Suggested Citation:"Chapter 3 - Demand." National Academies of Sciences, Engineering, and Medicine. 2013. Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook. Washington, DC: The National Academies Press. doi: 10.17226/22619.
×
Page 29
Page 30
Suggested Citation:"Chapter 3 - Demand." National Academies of Sciences, Engineering, and Medicine. 2013. Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook. Washington, DC: The National Academies Press. doi: 10.17226/22619.
×
Page 30

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

18 Demand General Public Rural Two methods are available to estimate the demand expected for passenger transportation in rural areas not related to social-service programs. A third method for estimation of demand for general public transportation (i.e., service used as reported to the rural NTD) also included in this section addresses demand based on need and the supply of service. This third method pro- vides a figure for demand that is not tied to a specific market, but provides an estimate for demand for transportation in general. The methods for general public (non-program) demand are listed below in order of suggested application: 1. Peer data from your system, other nearby systems or systems in same state or 2. Non-program Demand = (2.20 × Population age 60+) + (5.21 × Mobility Limited Population age 18 to 64) + (1.52 × Residents of Households having No Vehicle) Peer Data The preferred approach to estimating the demand for general public rural passenger trans- portation services is to base the estimate on the experience of your system, if one is operating, or the experience of other systems operating in similar rural settings in your own state. If there are few other systems in similar communities or regions within your state, you may need to obtain data from systems in adjacent states. To do this, you will want to obtain some information from the peer agencies so that their experience can be applied to your system. The information you will want is as follows (see Table 8): • Population of the area served • Size in square miles of the area served • Annual vehicle-miles and/or vehicle-hours of service provided • Nature of the operation (e.g., fixed-route, route-deviation, demand-response) • Number of one-way trips served (per month, per year) • Degree of coordination with other carriers From these data, compute such key ratios as • Passenger-trips per capita • Passenger-trips per vehicle-mile (by service type) • Passenger-trips per vehicle-hour (by service type) Compute these ratios for each peer system. Then determine the average value and the median value. (Note: The Excel functions =AVERAGE and =MEDIAN can be used to do this once the C H A P T E R 3

Demand 19 data are entered in an Excel spreadsheet. Other spreadsheet software will have similar functions.) Also determine the maximum and minimum values. Define your proposed operation in terms of • Population that will be served • Vehicle-miles that will be operated (per month, per year) • Vehicle-hours of service that will be operated (per month, per year) Fill in the cells in Table 9. In the row My System, enter the values for the population of your proposed service area and the number of vehicle-miles and/or vehicle-hours of service you pro- pose to operate. In the column, Trip Rates, enter the values of trips per unit (population, miles, hours) deter- mined from the identified peer systems. Then multiply the value for your system (column) by the peer rate (row) and enter the value in the appropriate column (see Figure 16). For each column determine the maximum, average, median, and minimum values. This gives reasonable estimates of the range of trips that may be expected. NOTE: your best peer system is your own operation. If you are operating service and wish to analyze the effects of adding new service or reducing existing service, simply compute the rates per capita, per hour, and per mile for your current operations and apply them to the proposed revised service plan. If you provide different levels of service to different parts of your community, then you can use your own data to estimate how other parts of your service area will respond to a different level of service. If you have changed service levels in past years, the experience gained from those changes can be used to estimate planned changes. Input Data from Peer Transit Systems or Existing Transit Service Name of Peer System Population of Area Size of Area Served (Square Miles) Annual Vehicle-Miles of Service Provided Annual Vehicle-Hours of Service Provided Service Type (Fixed-Route, Route- Deviation, Demand-Response) Number of One-Way Trips Served per Year Degree of Coordination with Other Carriers (Circle One) Low Medium High Low Medium High Low Medium High Low Medium High Low Medium High Table 8. Worksheet for Peer System Data Collection.

20 Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation General Public (Non-program) Demand Function Based on analysis of data collected in workshops and reported to the Rural National Transit Database for 2009, the following function was developed to produce reasonable estimates of the demand for general public, or non-program, passenger transportation in rural areas: Non-program Demand (trips per year) = (2.20 × Population Age 60+) + (5.21 × Mobility Limited Population age 18-64) + (1.52 × Residents of Household Having No Vehicle) To apply the function for analysis or planning, simply determine how many persons are in each demographic group in your service area, multiply by the proper factor, and add the results together. The demographic data can be gathered from the American Community Survey, fol- lowing the steps outlined above for accessing ACS data for estimating need. The table numbers associated with each are • Persons Age 60+ – B01001 • Persons with a Mobility Limitation age 18-64 – S1810 • Persons residing in Households with No Vehicle Available* – B08201 Table 10 provides space to record the values above along with the factors that should be applied. It will be necessary to do some calculations to arrive at the necessary demographic figures required for this method due to the breakdown of figures by age and/or sex. Simple addition will provide the required numbers. My S ystem Population Annual Vehicle - miles Annual Vehicle - hours Peer Values Observed Trip Rates Demand Estimate Based On Population Annual Vehicle - miles Annual Vehicle - hours Trips per Capita Maximum Average Median Minimum Trips per Vehicle - mile Maximum Average Median Minimum Trips per Vehicle - hour Maximum Average Median Minimum Values E xpected F or M y S ystem Maximum Average Median Minimum Table 9. Worksheet for Application of Peer System Values.

Demand 21 * Table B08201 provides values for households with no vehicle available. In order to produce values for persons living in households with no vehicle, follow the procedure outlined above in the Population Segments Method for Estimating Need. Example Computation–General Public Demand Pull Table B01001 for the ACS from American FactFinder. The steps for using American Fact- Finder can be found in the section addressing the Example Computation – Population Segments Method. Once the results table has been retrieved, calculate the number of persons Age 60 and older (see Figure 17). This is accomplished by adding the figures for each of the age groups start- ing with “60 and 61 years” and ending with “85 years and over” for males and females together. Once data for persons age 60 and older have been gathered, go back to the table search and search for Table S1810 (see Figure 18). Steps for accomplishing this task can be found in the Figure 16. Example Computation to Derive Trip Rates for Peer Data Method. Column A (persons) Column B Factor Column C (A x B) Age 60+ 2.20 Mobility Limited age 18-64 5.21 Household with No Vehicle Available 1.52 Es�mated Demand (Sum of Column C) Table 10. Worksheet for Estimating General Public (Non-Program) Demand.

22 Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation section titled Example Computation – Population Segments Method. The figure for persons with a mobility limitation can be pulled from the figure for persons “with an independent living dif- ficulty.” Persons in this category are thought to be the group most likely to require passenger transportation services. Note: As of the development of this workbook, these data were only available in the 3-Year ACS dataset. Once more yearly ACS datasets have been collected and published, a 5-year dataset should be available and used in the future. Obtaining the number of persons resident in households with no vehicle available requires the most manipulation from the base table pulled from the ACS. The Example Computation – Population Segments Method section describes how to use the data from Table B08201 and put it into Table 11 to derive the number of persons resident in households with no vehicle available. An example of the calculation for the demand estimate can be found in Table 12, using the example data from above. Rural Public Transportation Demand (Not Market Specific) The methods described above may be used to estimate the demand for “non-program related passenger transportation” (i.e., transportation not resulting from participation in a particular Figure 17. ACS Table B01001 Results – Bedford County, VA (Example). No Vehicle Mul�plier Persons resident in households owning no vehicle 1-person household 789 1 789 2-person household 274 2 548 3-person household 112 3 336 4- or more person household 18 4 72 Total Persons 1,745 Table 11. Worksheet for Documenting Persons with Transportation Needs – Bedford County, VA (Example).

Demand 23 social-service program). Many rural passenger transportation agencies serve both “program” and “non-program” trips. These “General Public” trips are those that are reported to the Rural NTD. A method for estimating the demand for such “General Public” trips is presented that relates expected demand to the estimate of need (previously described) and the amount of service provided. This estimation function was developed using data from the 2009 Rural NTD and data from the ACS. This function accounts for the need for transportation services in a given area, regardless of the type of service needed and the amount of service provided. This method produces an estimate of how much demand will result related to the amount of service provided. Column A (persons) Column B Factor Column C (A x B) Age 60+ 14,697 2.20 32,333 Mobility Limited age 18-64 1,537 5.21 8,008 Household with No Vehicle Available 1,745 1.52 2,652 Es�mated Demand (Sum of Column C) 42,993 Table 12. Worksheet for Estimating General Public Demand – Bedford County, VA (Example). Figure 18. ACS Table S1810 Results – Bedford County, VA (Example).

24 Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation This method can also be used to compare the change in demand associated with an expansion or reduction in service. Use Table 13 to estimate demand. The function is as follows: Annual Demand on Rural Transportation Services = 2.44 × (Need 0.028) × (Annual Vehicle-miles0.749)1 Need is computed using the Mobility Gap method discussed above. The daily mobility gap should be multiplied by 300 to produce an annual trip need. Annual vehicle-miles can be the existing service provided or number proposed to be provided. This figure should include all vehicle-miles of service provided to the public, regardless of the type of service. Example Computation–Non-Market-Specific Rural Demand Table B08201 was pulled for Archuleta County, CO, for this example (Figure 19). See Appendix A for steps on how to access ACS data. The mobility gap for Archuleta County is 15,600 annual trips (65 × 0.8 × 300). The amount of service provided for Archuleta County, CO, was 167,531 annual revenue miles (Source: 2010 Rural NTD). The resulting demand for Archuleta County, regardless of market, is 26,160 (2.44 × (15,6000.028) × (167,5310.749)). Archuleta County’s transit service serves local ski resorts and does not likely demonstrate a typical amount of service or ridership for a rural area this size. Program (Sponsored) Trips Program Trips are defined as those trips that would not be made without the existence of a specific social-service program or activity. The distinguishing factor is that the trip time and destination are set not by the traveler, but by the agency sponsoring the trip. Equations were presented in TCRP Report 3 for use in estimating Program Trip demand based on specific Census data. These formulas can be accessed from TCRP Report 3 online. Given the high variance in program trip demand that was observed in data obtained since the publication of TCRP Report 3, it is recommended that better estimates can be derived by using specific information collected directly from individual programs. To develop an estimate of the demand for program trips begin by listing the known programs in your area. Obtain from the agencies providing these services the following data (use Table 14): • Number of program participants • Number of days per week that the program meets • The number of weeks per year the program is offered • The proportion of program participants who attend the program on an average day • The proportion of program participants who require transportation service. (It has been observed that some people use provided transportation even though they can drive and own a vehicle because the ride is considered a part of the social aspect of the program. These indi- viduals should be included in the proportion figure.) 1 Raising a number to a non-integer power can be done on most scientific calculators or any spreadsheet program. Annual Mobility Gap Annual Vehicle-miles Table 13. Worksheet for Estimating Rural Public Transportation Demand.

Figure 19. ACS Table B08201 Results – Archuleta County, CO (Example). Program Name How many par�cipants? How many events (per week)? What is the percentage of par�cipants who a�end on an average day? What is the percentage of par�cipants who are transit dependent or likely to use transit? How many weeks is the program offered (annually)? Result x 2 (trips per par�cipant) Table 14. Worksheet for Program Transportation Data.

26 Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation Once the above data has been collected, use the following equation to estimate demand: Number of Program Participants × Program Events per Week × the Proportion of Program Participants who attend the Program on an Average Day × the Proportion of Program Participants that are Transit Dependent or Likely to Use the Transit Service provided/funded by the Agency × the Number of Weeks per Year the Program is Offered × 2 (trips per participant per event) Example Computation–Program Trips Table 15 shows data for a meal program as an example calculation using the method above. The resulting program would result in a demand of 6,310 annual trips. These trips could be served by the agency providing the program directly or coordinated with another program agency or a public transportation provider based on available capacity. Small City Fixed-Route In many rural counties there exist one or more small cities in which a traditional fixed-route, fixed-schedule transit service is operated. Analysis of data from the Rural NTD and data provided by representatives from agencies who attended workshops held as part of TCRP Project B-36 led to the following function for estimating ridership. This relationship demonstrates the impor- tance, in these small cities, of transit in supporting the local colleges and universities as well as the amount of service provided. The function for small city fixed-route service is Unlinked passenger-trips = 5.77 × Revenue-hours of Service + 1.07 × Population + 7.12 × College/ University Enrollment Conditions of application: Revenue-hours > 0; Population of urban center < 50,000. Does not include community college enrollment. To develop an estimate of demand, complete Table 16. Program Name Meal Program A How many par�cipants? 30 How many events (per week)? 3 What is the percentage of par�cipants who a�end on an average day? 90% What is the percentage of par�cipants who are transit dependent or likely to use transit? 75% How many weeks is the program offered (annually)? 52 Result x 2 6,319 annual trips Table 15. Worksheet for Program Transportation Data (Example).

Demand 27 Use the total enrollment, summed over all institutions, for either the current year or the plan- ning year in the equation above to estimate the ridership that can be expected on a small fixed-route system in an area of less than 50,000 population and less than 70 vehicle-hours of service per day. This method was developed using information from the Rural NTD. The data used were restricted to the mode coded MB (Motor bus) but both the “fixed-route” and “deviated fixed- route” data were included. The method may properly be applied to any small city operation that is either fixed-route or deviated fixed-route. Also, although colleges and universities are transit trip generators included in the recom- mended estimation method, other entities (e.g., military bases or national laboratories) located in rural settings may be of importance in other areas. Population figures for any city for which an estimate is being prepared can be gathered from several sources. The local planning department or regional planning agency will likely have fig- ures for population. Additionally, the ACS can be used to pull Census population figures. Table B01003 can be used to gather total population for a city or town from the ACS. Example Computation–Small City Fixed-Route Cortland, NY, is used for this example. Cortland is home to SUNY Cortland and has a popula- tion under 50,000. SUNY Cortland’s most recent enrollment figures show a student population of 7,358 (source: www.cortland.edu). According to the 2010 rural NTD, First Transit-Cortland provided 19,857 revenue-hours of service. The total population for Cortland can be pulled from the ACS. Following the steps for accessing data in Appendix A and using Table B01003 will yield a population figure of 19,257 (Figure 20). Using the figures reported above in the example and the formula for estimating demand for small city fixed-route service yields the following result: Unlinked passenger-trips = 5.77 × Revenue-hours of Service + 1.07 × Population + 7.12 × College/ University Enrollment = 5.77 × 19,857 + 1.07 × 19,257 + 7.12 × 7,358 = 187,569 Name of first university Name of second university Name of first college Etc. Totals Name of Ins�tu�on Current Enrollment (FTEs) Projected Planning Year Enrollment (FTEs) Table 16. Worksheet for College and University Enrollment Data. Source: U.S. Census Bureau, 2006-2010 American Community Survey Figure 20. ACS Table B01003 Results – Cortland, NY (Example).

28 Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation Commuters to Urban Centers The function developed for estimating the demand for commuter passenger transportation from a rural county to another county is given by Commuter trips by transit from County to Urban Center per Day = Proportion Using Transit for Commuter Trips from Rural County to Urban Place × Number of Commuters × 2 Proportion Using Transit for Commuter Trips from Rural County to Urban Place = 0.024 + (0.0000056 × Workers Commuting from Rural County to Urban Place) - (0.00029 × Distance in Miles from Rural County to Urban Place) + 0.015 (if the Urban Place is a state capital) In this function, the number of trips constituting the market for passenger transportation is directly related to the total commuting market. That value must be obtained from other sources. Information on current and forecast county-to-county commuter flows can be obtained from various sources, including data from the MPO for the urban center or the state transportation agency. Historic data on commuter flows in recent years are available from the US Census Bureau in either the Longitudinal Employer-Household Dynamics (LEHD) program (http://lehd.did. census.gov/led/) or the Journey-to-work tables from the ACS (http://factfinder2.census.gov/). Tables B08007 – Sex of Workers by Place of Work and B08406 – Sex of Workers by Means of Transportation to Work should provide sufficient data from the ACS. Although both the LEHD and ACS provide estimates of commuting patterns, the two datasets are developed in different ways and can present different results. The LEHD dataset is derived based on a greater proportion of the workers in any given area. As a result it is likely to give a more accurate representation of commuter flows from areas that have smaller populations (e.g., rural areas). As noted in an NCHRP publication NCHRP08-36 Task 98: Unlike sample-based surveys (such as the CTPP), the LEHD-OTM provides a (nearly) complete enumeration of home-to-work flows covering over 90 percent of all workers and employers in the United States. As such, it includes many more OD pairs containing low frequency home-to-work flows than are collected through sampled data. See http://onlinepubs.trb.org/onlinepubs/nchrp/docs/NCHRP08-36(98)_FR.pdf for a dis- cussion of the use of both LEHD data and ACS data. This LEHD website allows the analyst to specifically define the residential area and see the commuter flows to various employment areas. Data can be further aggregated by job type, worker age, earnings level, and industry class. Information on current and projected county-to-county commuter flows may also be avail- able from the MPO serving the urban center or from your state transportation agency. Example Computation–Commuters to Urban Centers Go to http://lehd.did.census.gov/led/ (Figure 21). Click the OnTheMap link in the upper left of the screen. Once the OnTheMap application is up (Figure 22), search for the rural county where workers will be traveling from and click Search. Select the appropriate county if multiple counties of the same name appear in the search. The program will then highlight the area you have selected on the map to the right and bring up a popup with some general information about the county and an option to Perform Analysis on Selection Area. Click this link. Once Perform Analysis on Selection Area is clicked, another window will pop up for the Analysis Settings (Figure 23). Select Home for Home/Work Area, indicating your interest is on residents

Demand 29 Figure 21. LEHD Main Page. Figure 22. LEHD Search Page. Figure 23. LEHD Analysis Settings.

30 Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation who live in the area/county. Select Destination for Analysis Type, which will identify the place people travel from their home to work. The drop-down menu should read Places (Cities, CDPs, etc.). This will determine the urban center. Select the most current year available for Year. Then select Primary Jobs for Job Type. This will provide a county of the primary job everyone travels to and will not count second jobs people might work. This is believed to be the better definition of the types of jobs suitable for commuter service. Then click Go. The results screen (Figure 24) will include a map as well as the count of jobs for each area held by someone in the rural county. This will be used as the number of commuters traveling from a rural county to an urban place. To calculate the demand in number of trips that would occur by transit between a rural county and urban place, it is necessary to calculate the proportion of commuters from a rural county to an urban place using transit. The formula is as follows: Proportion using Transit for Commuter Trips from Rural County to Urban Place = 0.024 + (0.0000056 × Workers Commuting from Rural County to Urban Place) - (0.00029 × Distance in Miles from Rural County to Urban Place) + 0.015 (if the Urban Place is a state capital) = 0.024 + (0.0000056 × 1,450) - (0.00029 × 22) = 0.026 The number of workers commuting from a rural county to an urban place is taken from the LEHD results. The distance in miles from the rural county to the urban place can be estimated using a mapping program such as Google Maps. If the urban place is a state capital, then the final figure in the formula is added. If not, then nothing is done. Once a proportion using transit figure is calculated, it can be plugged into the demand formula below to get a number of trips that would occur daily. Commuter trips by transit from County to County per Day = Proportion using transit for Commuter Trips from Rural County to Urban Place × Number of Commuters × 2 = 0.026 × 1,450 × 2 = 75 Multiplying the daily result by 255 will produce an estimate for annual trips from a rural county to an urban center. The annual number of trips from Fluvanna County to Charlottesville, VA, is likely to be around 19,227. Figure 24. LEHD Results – Fluvanna County, VA (Example).

Next: Chapter 4 - Data Sources »
Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook Get This Book
×
 Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook
Buy Paperback | $52.00
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

TRB’s Transit Cooperative Research Program (TCRP) Report 161: Methods for Forecasting Demand and Quantifying Need for Rural Passenger Transportation: Final Workbook presents step-by-step procedures for quantifying the need for passenger transportation services and the demand that is likely to be generated if passenger transportation services are provided.

The report is supplemented by two products: an Excel spreadsheet that can be used to implement the procedures included in the workbook; and a methodology report, TCRP Web-Only Document 58, which documents how the research team developed the need and demand estimation methods, the findings of the analyses, and recommendations for functions to be used in estimation of need and demand.

The Excel spreadsheet is available for download only from TRB’s website.

Excel Spreadsheet Disclaimer - This software is offered as is, without warranty or promise of support of any kind either expressed or implied. Under no circumstance will the National Academy of Sciences or the Transportation Research Board (collectively "TRB") be liable for any loss or damage caused by the installation or operation of this product. TRB makes no representation or warranty of any kind, expressed or implied, in fact or in law, including without limitation, the warranty of merchantability or the warranty of fitness for a particular purpose, and shall not in any case be liable for any consequential or special damages.

READ FREE ONLINE

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  6. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  7. ×

    View our suggested citation for this chapter.

    « Back Next »
  8. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!