National Academies Press: OpenBook

Traffic Signal Control Strategies for Pedestrians and Bicyclists (2022)

Chapter: Chapter 3 - Performance Measures Related to Serving Pedestrians and Bicyclists

« Previous: Chapter 2 - Understanding User Needs and Establishing Priorities
Page 11
Suggested Citation:"Chapter 3 - Performance Measures Related to Serving Pedestrians and Bicyclists." National Academies of Sciences, Engineering, and Medicine. 2022. Traffic Signal Control Strategies for Pedestrians and Bicyclists. Washington, DC: The National Academies Press. doi: 10.17226/26491.
×
Page 11
Page 12
Suggested Citation:"Chapter 3 - Performance Measures Related to Serving Pedestrians and Bicyclists." National Academies of Sciences, Engineering, and Medicine. 2022. Traffic Signal Control Strategies for Pedestrians and Bicyclists. Washington, DC: The National Academies Press. doi: 10.17226/26491.
×
Page 12
Page 13
Suggested Citation:"Chapter 3 - Performance Measures Related to Serving Pedestrians and Bicyclists." National Academies of Sciences, Engineering, and Medicine. 2022. Traffic Signal Control Strategies for Pedestrians and Bicyclists. Washington, DC: The National Academies Press. doi: 10.17226/26491.
×
Page 13
Page 14
Suggested Citation:"Chapter 3 - Performance Measures Related to Serving Pedestrians and Bicyclists." National Academies of Sciences, Engineering, and Medicine. 2022. Traffic Signal Control Strategies for Pedestrians and Bicyclists. Washington, DC: The National Academies Press. doi: 10.17226/26491.
×
Page 14
Page 15
Suggested Citation:"Chapter 3 - Performance Measures Related to Serving Pedestrians and Bicyclists." National Academies of Sciences, Engineering, and Medicine. 2022. Traffic Signal Control Strategies for Pedestrians and Bicyclists. Washington, DC: The National Academies Press. doi: 10.17226/26491.
×
Page 15
Page 16
Suggested Citation:"Chapter 3 - Performance Measures Related to Serving Pedestrians and Bicyclists." National Academies of Sciences, Engineering, and Medicine. 2022. Traffic Signal Control Strategies for Pedestrians and Bicyclists. Washington, DC: The National Academies Press. doi: 10.17226/26491.
×
Page 16
Page 17
Suggested Citation:"Chapter 3 - Performance Measures Related to Serving Pedestrians and Bicyclists." National Academies of Sciences, Engineering, and Medicine. 2022. Traffic Signal Control Strategies for Pedestrians and Bicyclists. Washington, DC: The National Academies Press. doi: 10.17226/26491.
×
Page 17
Page 18
Suggested Citation:"Chapter 3 - Performance Measures Related to Serving Pedestrians and Bicyclists." National Academies of Sciences, Engineering, and Medicine. 2022. Traffic Signal Control Strategies for Pedestrians and Bicyclists. Washington, DC: The National Academies Press. doi: 10.17226/26491.
×
Page 18
Page 19
Suggested Citation:"Chapter 3 - Performance Measures Related to Serving Pedestrians and Bicyclists." National Academies of Sciences, Engineering, and Medicine. 2022. Traffic Signal Control Strategies for Pedestrians and Bicyclists. Washington, DC: The National Academies Press. doi: 10.17226/26491.
×
Page 19

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.

11   In the outcome-based approach introduced in the previous chapter, the next step after defining and prioritizing user needs is to define performance measures—also known as measures of effec- tiveness (MOEs)—that indicate the degree to which user needs and operational objectives are met. Performance data on existing conditions can be used to identify unmet needs. In the design stage, performance data can be used to optimize and compare alternatives; after improvements are made, they can be used for before-and-after analysis. An outcome-based approach can also help document decisions and emphasize agency priorities and community values when consid- ering trade-offs in decision-making. This outcome-based approach is well-established for serving vehicular intersection users, and intersection designers pay careful attention to performance measures such as volume/capacity ratio, average vehicular delay, and level of service. Pedestrians and cyclists require the same level of attention to adequately address their needs. The following sections provide details on performance measures, including data such as counts and crash statistics, that are also used to quantify user needs. 3.1 Crash and Other Safety Data Crash data is critical for assessing intersection performance relative to safety risks and diag- nosing outcomes that a change in intersection design and/or operations might address. Prac- titioners can obtain 3–5 years of crash data and summarize the crashes by type, severity, and environmental conditions (e.g., day/night, raining). A collision diagram as shown in Exhibit 3-1 can help identify trends. Crash statistics can tell an incomplete story about the safety of pedestrians and cyclists in part because they experience far greater vulnerability than motorists, which leads them to avoid dangerous situations. Likewise, their nimbleness can enable them to avoid collisions in situa- tions that are nevertheless quite stressful. For this reason, site visits can be enormously valuable in helping practitioners identify undocumented needs as well as causal factors underlying crash statistics. Field observation may indicate where turns are made at unusually high speeds, where visibility is obstructed, or where pedestrians are unable to clear an intersection in time. It may reveal uncomfortable interactions with turning traffic, gaps in accessibility, or high-risk behav- iors that reveal an underlying flaw in the intersection design. A safe-systems approach acknowledges that crash counts alone are not sufficient to determine the underlying level of safety, particularly where pedestrian and bicycle volume is low. Even where there have been few crashes, trained observers may be able to note conditions that create a high risk of crashing. C H A P T E R 3 Performance Measures Related to Serving Pedestrians and Bicyclists

12 Trafc Signal Control Strategies for Pedestrians and Bicyclists Conict counts can also be used as a performance measure, both as a surrogate for non- motorized user crashes (which, fortunately, are rare events) and as a direct measure of perceived safety and comfort. For example, several of the treatments described in this guidebook aim to lessen conicts between pedestrians and turning vehicles; a count of how oen a pedestrian had to stop or changed course because of a non-yielding turning vehicle can be used as a per- formance measure related to that objective. Hubbard et al. (2007) measured the percentage of compromised pedestrian crossings and found that leading pedestrian intervals (LPIs) reduce the number of compromised crossings. Compliance counts can also be valuable safety measures. Poor red-light compliance by pedes- trians and bicyclists can indicate (1) poorly designed trac control with excessive pedestrian or bike delay or (2) signals that tell non-motorized users not to go even when it is safe to cross. Violations of no turn on red restrictions and drivers not yielding when making permissive turns (including when turning on red) can indicate a need for stronger messaging or intersection design changes. 3.2 Pedestrian, Bicycle, and Conicting Vehicle Counts Counts of pedestrians, bicycles, and conicting trac movements can be helpful for evalu- ating needs, establishing priorities, choosing signalization treatments, and evaluating perfor- mance. Whenever intersection turning movements are counted, agencies should also count pedestrians by crosswalk and bicyclists by movement. Pedestrian counts can be used, for example, to help determine whether a pedestrian phase should be pushbutton actuated or on recall and to evaluate average pedestrian delay aggregated over the dierent crosswalks at an intersection. High pedestrian-volumes can trigger a need to analyze crowding in the crosswalk or in queuing areas. Counts of conicting trac movements help determine whether a fully or partially protected crossing treatment, such as LPI, may be warranted. Geometric elements of a crossing, including crossing islands and corner queuing areas, must be sized for a signal cycle with high demand. Where pedestrian or bicycle demand has peri- odic surges—such as at schools or at sports or entertainment venues—volumes per hour are Source: Urbanik et al. (2015), Exhibit 3-16. Exhibit 3-1. Example collision diagram.

Performance Measures Related to Serving Pedestrians and Bicyclists 13   misleading; counts are needed by minute or per signal cycle, and elements should be sized for a high-demand cycle. An important limitation of pedestrian and bicycle counts to consider is that they may not represent actual demand. An absence of non-motorized users could mean the intersection or streets leading to it are not hospitable or comfortable for non-motorized users, which suppresses demand. In addition, bicycle and pedestrian counts tend to be far more sensitive to weather, special events, the school calendar, and other local factors than vehicular counts. If pedestrian and bicycle counts were made in conjunction with vehicular counts and were done on days of unusual pedestrian or bicycle demand, then substitute counts may be needed for bicycles and pedestrians. 3.3 Average Pedestrian Delay As stated in Chapter 2, minimizing delay for all users is an important objective in intersection design; therefore, average delays of pedestrians and of bicycles are vital performance measures. Pedestrian and bicycle delays are important measures of safety performance as well as user con- venience because they are closely linked to noncompliance. Typical intersection design practice has not included measurement or reporting of pedestrian delay. For pedestrian delay to be optimized and prioritized—as vehicular delay is—it must be measured and reported as part of the intersection design process. By establishing policies to ensure that pedestrian delay is reported, agencies can go a long way toward achieving intersec- tion designs that are more pedestrian-friendly. Commonly used intersection analysis software does not calculate or report pedestrian delay, even though the software recommends a pedestrian signal timing and has all the data needed to calculate pedestrian delay. Therefore, if agencies begin requiring that pedestrian delay be reported, designers will have to calculate pedestrian delay in a separate analysis and provide it separately from standard reports produced by intersection analysis software. To consolidate the reporting process, agencies that specify or recommend any particular intersection analysis software should consider demanding that its developers add pedestrian and bicycle delays to its calculation and reporting functionality. 3.4 Pedestrian Delay Formulas for Pretimed, Actuated, and Multistage Crossings For single-stage crossings with pretimed signals, the 2016 Highway Capacity Manual: A Guide for Multimodal Mobility Analysis (HCM6) provides a well-established formula for pedestrian delay in Equation 3-1: ( )= − 2 (3-1) 2 d C g Cp Walk where dp = average pedestrian delay, C = cycle length, and gWalk = the effective Walk interval. HCM6 suggests including additional Walk time on top of actual Walk time as the effec- tive Walk interval, recognizing that many pedestrians begin to cross in the first few seconds

14 Traffic Signal Control Strategies for Pedestrians and Bicyclists of the Flashing Don’t Walk (FDW) interval. Equation 3-2, the effective Walk interval gWalk, makes use of this: = + additional Walk time (3-2)g WALKWalk where WALK = the length of the Walk interval. HCM6 suggests using 4 s as additional Walk time based on a study that predates pedestrian countdown timers. For pedestrian crossings that are pushbutton actuated, the HCM6 delay formula underesti- mates average pedestrian delay because—unless someone who arrived earlier has pushed the button—a pedestrian arriving during the scheduled Walk interval will find the pedestrian signal in its solid Don’t Walk aspect and will have to wait for the next cycle for a Walk indication. If demand is low enough that any arriving pedestrian is likely to be the only one using that crosswalk in a cycle, average delay with pushbutton actuation is given by Equation 3-3: = 2 (3-3)d Cp This equation is a good approximation when there are fewer than one pedestrian per four cycles. The extra delay or “delay penalty” due to requiring pedestrian actuation can be substantial. For example, suppose the cycle length is 100 s, the Walk interval is 7 s, and pedestrian demand is very low. In this case, average delay with actuated control is 10 s longer than it would be with pretimed control. If pedestrian demand is high, then the pedestrian phase will come up almost every cycle; pedestrians arriving “just too late” to get a Walk signal in the current cycle if they had to push the button themselves are likely to have been preceded by others who have already pushed the button. For crosswalks with demand of three pedestrians per cycle or greater, the formula for fixed time control (Equation 3-1) is a good approximation. For intermediate levels of pedestrian demand, practitioners can interpolate between the results given by Equations 3-1 and 3-3. Let: vP = demand for a particular crosswalk (both directions) [pedestrians/hour (h)], vPlo = 900/C = demand at which Equation 3-3 applies (pedestrians/h), vPhi = 10,800/C = demand at which Equation 3-1 applies (pedestrians/h), dpre = average delay assuming pretimed control, given by Equation 3-1 (s), dal = average delay for pushbutton-actuated control under very low demand, given by Equa- tion 3-3 (s), and d = average delay (s). Then delay for a pushbutton-actuated crossing can be approximated by: ( ) = ≤ = ≥ + − − − if , if , and otherwise, = 1 1 1 1 (3-4) d d vP vP d vP vP d d d vP vP vP vP p al lo pre hi pre al pre hi lo hi

Performance Measures Related to Serving Pedestrians and Bicyclists 15   For crossings that have to be made in two or more stages, pedestrian delay can be decep- tively long and complex to calculate by formula (Wang & Tian, 2010; Ma et al., 2011). Instead, a simple numerical method can be applied that divides the signal cycle into 0.1-second time steps, tracks the delay a pedestrian arriving in a given time step would experience while crossing, and averages the results over all time steps (Furth et al., 2019). is method can be applied using the Northeastern University Ped & Bike Crossing Delay Calculator, which is available for free at https://peterfurth.sites.northeastern.edu/2014/08/02/ delaycalculator/ (Furth et al., 2019). e calculator can handle up to four crossing stages as well as partial crossing phases that are served twice in a cycle. A user enters crosswalk geometry and pedestrian timing data through a graphical interface; the tool then reports average pedestrian delay for both directions, including average delay at each island, and generates a progres- sion diagram. Exhibit 3-2 shows a sample report for a three-stage crossing in Boston, MA. Note that the average delay in Exhibit 3-2 is more than 120 s, even though the cycle length is only 100 s. A new Highway Capacity Manual (HCM) procedure and computational engine for mea- suring pedestrian delay at multistage crossings has also been developed (Ryus et al., in press), which will be included in an update of the HCM that was in publication at the time of writing. It is also possible to calculate average pedestrian delay using microsimulation models that include pedestrian modeling functionality. However, this method involves considerable time and expertise as well as the cost of the soware license. If microsimulation is used, it is important to run the model long enough for it to process at least 500 pedestrians per crosswalk; this will Source: Furth et al. (2019). Exhibit 3-2. Delay report and progression diagram for a three-stage pedestrian crossing.

16 Traffic Signal Control Strategies for Pedestrians and Bicyclists reduce variability and capture a sufficient sample size since individual delay varies depending on when in the cycle a person arrives. 3.5 Bicycle Delay and Average Operating Speed In many cases, bicycle delay closely tracks with vehicular delay or pedestrian delay. Where bicycles follow vehicular signals, bicycle delay is usually a little less than the delay of the concur- rent vehicular movement if signalized intersections are widely spaced. This is because bicycles usually have little queue delay once the traffic signal turns green. Where bicycles follow a pedes- trian phase, their delay will be a little less than pedestrian delay because cyclists usually begin to cross not only during the Walk interval but also during the FDW interval. Nevertheless, bicycle delay should be considered as a key performance measure along with average operating speed, which applies to corridors with closely spaced signals. This guidebook highlights some common situations in which bicycle delay can be substan- tially different from either pedestrian or vehicle delays. One such situation is a street with closely spaced signals, as discussed in Section 9.2. Depending on the progression speed represented by the signal offsets, bicycles may or may not be able to stay in the “green wave,” affecting their average operating speed. Another situation occurs when bicycles make a two-stage left turn (two square crossings, in which they stay on the outside of the intersection) rather than making a vehicular turn as discussed in Section 9.3. Bicycle delay will also depend on whether bicycles are allowed to use LPIs (see Section 6.5) or turn right on red (see Section 9.6). 3.6 Accessibility and Intersection Layout Measures There are several indicators—in addition to the accessibility of signals—that can be measured in order to make crossings accessible, including: • Lowest pedestrian speed designed (see Section 7.4). • Distance between accessible pushbuttons serving different crosswalks at a single corner. The minimum separation specified by the United States Access Board public rights-of-way accessibility guidelines (U.S. Access Board, 2011) is 10 ft, but separation greater than 10 ft is preferred (see Section 8.3). • Pushbutton offset from a crosswalk’s approach path and from the curb (see Section 8.3; Section 9.4). Other performance measures related to a crossing’s physical layout include: • Crosswalk length and related adequacy of clearance time provided (see Section 7.4). • Depth of a crossing island and queuing area on an island versus the depth and area needed; the dimensions needed by bicycles are different from those needed by pedestrians (see Section 10.1). • Sight distance for permitted-turn conflicts when a bicycle path is physically separated from a roadway (see Section 6.1). 3.7 Performance Data from Traffic Signal Systems Centralized signal systems capable of automatically logging data offer the potential to gen- erate useful performance measures from the data. Systems that have high-resolution data-logging capabilities are especially promising.

Performance Measures Related to Serving Pedestrians and Bicyclists 17   3.7.1 Using Centralized Signal Systems Many agencies utilize centralized traffic signal systems with the capability to log data automat- ically and generate reports with various performance measures. Typically, data is often used for monitoring and maintenance, but it can also be used to support a performance-based improve- ment process. These central systems can generate system reports, which typically include various historical reports and MOEs. The reports can be predefined—with reporting intervals selected by the user—or they can be scheduled to run automatically. Some examples of these reports include vehicle detector occupancy, green time distribution, vehicle detector failures, and the number of max outs. While traditionally the measures are more focused on vehicular performance, pedestrian volume and pedestrian detector failures can also be generated from some of the central systems and can be utilized by practitioners. In addition, customized reports and network alerts can be generated with some of these systems to gain better understanding of pedestrian and bicycle operations. For example, Clark County, WA, often programs phase splits that are less than the time required to serve pedestrians in order to maintain shorter cycle lengths and reduce delay for all users. When there is a pedestrian call, the phase is lengthened to serve it; the cycle is then forced into a transition period to recover the extra time used by the lengthened phase in order to become coordinated again. Staff members can create a summary report from the central system to identify the frequency of transitions due to a pedestrian call. At intersections where transitions occur more frequently and disrupt signal coordination, signal timing strategies are reviewed and adjusted to serve pedestrian timings within the coordinated cycles. This review process limits transitions, improves service for pedestrians, and reduces the impact on signal coordination. 3.7.2 Using High-Resolution Signal Controller Data High-resolution detector and signal-state data can be used to automatically generate a range of signalized intersection performance measures called automated traffic signal performance measures (ATSPMs). High-resolution controller event data consist of time-stamped logs of “events” occurring in a signal controller, including detector input and signal-state changes, with a time resolution of a tenth of a second or smaller. ATSPMs are already being used by sev- eral agencies, and the Utah Department of Transportation (UDOT) developed an open-source platform that can create a series of visual reports utilizing the high-resolution data from signal controllers. While ATSPM development has mainly focused on measures that serve vehicles, ATSPMs can also be used for measures that serve pedestrians and bicycles. The UDOT platform includes a Pedestrian Delay report that displays the delay between actuation of a pedestrian call and the start of the next Walk indication. This measure is closely related to average pedestrian delay; however, they are not identical because the delay of pedestrians arriving after another pedestrian has made a call is not accounted for. UDOT’s Pedestrian Delay report also displays the total number of pedestrian actuations (Exhibit 3-3), which is closely related to pedestrian demand. (However, as mentioned previ- ously they are not the same because pedestrians arriving after the pedestrian phase has been called are not counted.) By indicating how often pedestrian phases are needed, the frequency of pedestrian actuations can also be helpful in designing signal timing plans. When the frequency is low, designers may use a shorter cycle length than what would be needed to account for a full set of pedestrian phases. With this kind of timing, the cycle will be lengthened whenever a pedestrian phase is served; then a transition routine is run to recover the extra time added to

18 Trafc Signal Control Strategies for Pedestrians and Bicyclists the cycle and thus restore the intersection to coordination. When the frequency of pedestrian actuations is low, this practice can reduce delay for both pedestrians and vehicles, and it can be especially valuable when applied to a critical intersection whose cycle length governs the cycle length of a corridor. However, if the frequency of pedestrian actuations is too high, this strategy becomes inecient due to the frequent transitions. Unfortunately, reports based on pedestrian phase actuation data are unable to measure pedes- trian activity or delay if pedestrian phases are on recall, and their accuracy in measuring pedestrian delay and activity declines when pedestrian volume is high enough that crosswalks serve multiple pedestrians per cycle. High-resolution controller data can also be used to generate performance measures related to conicts between pedestrians and permitted turns (either right-turn or le-turn movements). At intersections with lane-specic vehicle count detectors, which are typically located just past the stop bar, counts of permitted-turning movements can be collected by cycle. When the pedes- trian phase is actuated, counts during cycles with registered pedestrians can then be isolated. An example in Exhibit 3-4 shows right-turn vehicular ow rates by cycle, limited to cycles in which the pedestrian phase is served, for two dierent days on a college campus. August 13 (blue) was one week prior to the start of classes, and August 22 (red) was during the rst week of classes (Hubbard et al., 2008). e data are sorted from largest to smallest ow rate. e increase in right-turn volume aer classes began is evident. is analysis shows that aer classes began, there were 15 cycles per day with pedestrian activity, and conicting trac volume in those cycles was 1,200 vehicles per hour or greater; this corresponds to an average headway of less than 3 s between vehicles. is analysis helped support a decision to implement an exclusive pedestrian phase. Exhibit 3-3. Pedestrian Delay report example generated by the UDOT open-source platform.

Performance Measures Related to Serving Pedestrians and Bicyclists 19   Bibliography Furth, P. G., Wang, Y. D., & Santos, M. A. (2019). Multi-Stage Pedestrian Crossings and Two-Stage Bicycle Turns: Delay Estimation and Signal Timing Techniques for Limiting Pedestrian and Bicycle Delay. Journal of Trans- portation Technologies, 9(04), 489–503. Highway Capacity Manual: A Guide for Multimodal Mobility Analysis, 6th Edition. (2016). Transportation Research Board, Washington, DC. Hubbard, S. M. L., Awwad, R. J., & Bullock, D. M. (2007). Assessing the Impact of Turning Vehicles on Pedes- trian Level of Service at Signalized Intersections: A New Perspective. Transportation Research Record: Journal of the Transportation Research Board, 2027(1), 27–36. Hubbard, S. M. L., Bullock, D. M., & Day, C. M. (2008). Integration of Real-Time Pedestrian Performance Mea- sures into Existing Infrastructure of Traffic Signal System. Transportation Research Record: Journal of the Transportation Research Board, 2080(1), 37–47. Ma, W., Liu, Y., Xie, H., & Yang, X. (2011). Multiobjective Optimization of Signal Timings for Two-Stage, Mid- block Pedestrian Crosswalk. Transportation Research Record: Journal of the Transportation Research Board, 2264(1), 34–43. Ryus, P., Musunuru, A., Bonneson, J., Kothuri, S., Monsere, C., McNeil, N., LaJeunesse, S., Nordback, K., Kumfer, W., & Currin, S. (in press). NCHRP Research Report 992: Guide to Pedestrian Analysis. Transporta- tion Research Board, Washington, DC. Urbanik, T., Tanaka, A., Lozner, B., Lindstrom, E., Lee, K., Quayle, S., Beaird, S., Tsoi, S., Ryus, P., Gettman, D., Sunkari, S., Balke, K., & Bullock, D. (2015). NCHRP Report 812: Signal Timing Manual, 2nd Edition. Trans- portation Research Board, Washington, DC. U.S. Access Board. (2011). (Proposed) Public Rights-of-Way Accessibility Guidelines. Washington, DC. Wang, X., & Tian, Z. (2010). Pedestrian Delay at Signalized Intersections with a Two-Stage Crossing Design. Transportation Research Record: Journal of the Transportation Research Board, 2173(1), 133–138. Source: Hubbard et al. (2008). 0 200 400 600 800 1000 1200 1400 1600 1800 0 10 10020 30 40 50 60 70 80 90 Cycles with Pedestrian Actuation RT F lo w R at e du rin g Pe d In te rv al (v ph ) August 13, 2007 August 22, 2007 15 Cycles with the Highest Vehicular Flow Rates 1200 Vehicles/Hour Corresponds to 3-Second Average Headways for Vehicles Turning Right Across a Pedestrian Movement Exhibit 3-4. Pedestrian conflicts example: Right-turn vehicular flow rates during cycles with pedestrian actuations.

Next: Chapter 4 - Signal Timing Basics »
Traffic Signal Control Strategies for Pedestrians and Bicyclists Get This Book
×
 Traffic Signal Control Strategies for Pedestrians and Bicyclists
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

In the United States, traffic signal timing is traditionally developed to minimize motor vehicle delay at signalized intersections, with minimal attention paid to the needs of pedestrians and bicyclists. The unintended consequence is often diminished safety and mobility for pedestrians and bicyclists.

The TRB National Cooperative Highway Research Program's NCHRP Research Report 969: Traffic Signal Control Strategies for Pedestrians and Bicyclists is a guidebook that provides tools, performance measures, and policy information to help agencies design and operate signalized intersections in a way that improves safety and service for pedestrians and bicyclists while still meeting the needs of motorized road users.

Supplemental to the report are presentations of preliminary findings, strategies, and summary overview.

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!