Assured clear distance ahead

As a corollary to the rule that drivers generally must not pose an "immediate hazard" upon where or when they cannot assure such distance ahead is clear, it follows that others may presume that no vehicle is posing an "immediate hazard" from beyond where they can see with proper lookout. Where there are cross roads or side roads with view obstructions, the assured clear distance terminates at the closest path of potential users of the roadway until there is such a view which assures the intersection will remain clear. In such situations, approach speed must be reduced in preparation for entering or crossing a road or intersection or the unmarked pedestrian crosswalks

Horizontal clearance is measured from the edge of the traveled way to the bottom of the nearest object, tree trunk or shrub foliage mass face, plant setback, or mature growth.[106]^[138] Horizontal sight distance is not to be confused with the clear recovery zone which provides hazardous vegetation set-back to allow errant vehicles to regain control, and is exclusive to a mowed and limbed-up forest which can allow adequate sight distance, but unsafe recovery.^[138] The height and lateral distance of plants restrict the horizontal sight distance, at times obscuring wildlife which may be spooked by an approaching vehicle and run across the road to escape with their herd.^[113][138] This principle also applies to approaching vehicles and pedestrians at uncontrolled intersections and to a lesser degree by un-signalized intersections controlled by a yield sign. Horizontal sight distance "d_hsd" affects the ACDA because the time t_i=d_hsd/V_i it takes for an intercepting object, animal, pedestrian, or vehicle with speed "V_i" to transverse this distance after emerging from the proximate edge of lateral visibility affords a vehicle with speed "V" a clear distance of "V*t_i". Thus, the assured clear intercept distance "ACDA_si" is:

${\displaystyle ACDA_{si}={\frac {Vd_{hsd}}{V_{i}}}}$

The faster one drives, the farther down-road an interceptor must be in order to be able to transverse the horizontal sight distance in time to collide, however this says nothing of whether the vehicle can stop by the end of this type of assured clear distance. Equating this distance to the total stopping distance and solving for speed yields one's maximum

Dynamic "following" distance

The ACDA may also be dynamic as to the moving distance past which a motorist can be assured to be able to stay clear of a foreseeable dynamic hazard—such as to maintain a distance as to be able to safely swerve around a bicyclist should he succumb to a fall—without requiring a full stop beforehand, if doing so could be exercised with

Drivers need not and are not required to precisely determine the maximum safe speed from real-time mathematical calculations of sight distances and stopping distances for their particular vehicle.[118] Motor vehicle operators of average intelligence^[81][141] are constantly required to utilize their kinesthetic memory in all sorts of driving tasks including every time they brake to a full stop at a stop line in a panoply of conditions.^[53][142] Like throwing a softball, one does not have to mathematically calculate a trajectory or firing solution in order to hit a target with repeated accuracy. During the earliest stages of learning how to drive, one develops a memory of when to start braking (how long it takes) from various speeds in order to stop at the limit line.^[142] While there may be a degree of variance of such skill in seasoned drivers, they generally do not have the discretion in engaging in a behavior such as driving a speed above which no reasonable minds might differ as to whether it is unsafe or that one could come to a stop within the full distance ahead.^[126][141]

Seconds of distance to stop rule

Drivers and law enforcement alike can apply elementary level arithmetic^[143] towards a rule of thumb to estimate minimal stopping distance in terms of how many seconds of travel ahead at their current speed. For speed "v" in miles per hour, this rule of thumb is as follows:

${\displaystyle \color {Sepia}{t\approx {\frac {v}{20}}+1\quad {\text{(seconds of distance to stop rule)}}}}$

If this distance is greater than the ACDA, they need to decelerate. While most experienced drivers develop a broad

ACDA rule-specific case generalized to the Basic Speed Law

The ACDA distances are a principal component to be evaluated in the determination of the maximum safe speed (V_BSL) under the basic speed law, without which the maximum safe speed cannot be determined. As mathematical statements are more precise than verbal statements alone,^[144] the relation of the ACDA as a subset of the basic speed rule for land based vehicles may be objectively quantified as follows:

${\displaystyle V_{BSL}={\begin{cases}{\sqrt {(\mu +e)^{2}g^{2}t_{prt}^{2}+2(\mu +e)gd_{ACDA_{s}}}}-(\mu +e)gt_{prt},&{\text{if }}V_{ACDA_{s}}\leq V_{ACDA_{si1}}{\text{ or }}V_{ACDA_{si2}}{\text{ or }}V_{ACDA_{d}}{\text{ or }}V_{cs}{\text{ or }}V_{cl}\\\\2g(\mu +e)({\frac {d_{hsd}}{v_{i}}}-t_{prt}),&{\text{if }}V_{ACDA_{si1}}<V_{ACDA_{s}}{\text{ or }}V_{ACDA_{si2}}{\text{ or }}V_{ACDA_{d}}{\text{ or }}V_{cs}{\text{ or }}V_{cl}\\\\2g(\mu +e)\left({\sqrt {\frac {2d_{sl}}{a_{i}}}}+t_{pc}-t_{prt}\right),&{\text{if }}V_{ACDA_{si2}}<V_{ACDA_{s}}{\text{ or }}V_{ACDA_{si1}}{\text{ or }}V_{ACDA_{d}}{\text{ or }}V_{cs}{\text{ or }}V_{cl}\\\\{\frac {d_{ACDA_{d}}}{t_{g}}},&{\text{if }}V_{ACDA_{d}}<V_{ACDA_{s}}{\text{ or }}V_{ACDA_{si1}}{\text{ or }}V_{ACDA_{si2}}{\text{ or }}V_{cs}{\text{ or }}V_{cl}\\\\{\sqrt {\frac {(\mu +e)gr}{1-\mu e}}},&{\text{if }}V_{cs}<V_{ACDA_{s}}{\text{ or }}V_{ACDA_{si1}}{\text{ or }}V_{ACDA_{si2}}{\text{ or }}V_{ACDA_{d}}{\text{ or }}V_{cl}\\\\V_{cl},&{\text{if }}V_{cl}<V_{ACDA_{s}}{\text{ or }}V_{ACDA_{si1}}{\text{ or }}V_{ACDA_{si2}}{\text{ or }}V_{ACDA_{d}}{\text{ or }}V_{cs}\end{cases}}}$

The value of the variable "e" is the

[Note 5]

The maximum velocity permitted by the Assured Clear Distance Ahead is controlling of safe speed (V_BSL) for only the top and two cases. Safe speed may be greater or less than the actual legal speed limit depending upon the conditions along the road.^[124]

^{[Note 6]}

See reference V_BSL derivations for basic physics explanation.

ACDA: forward line-of-sight

For the top case, the maximum speed is governed by the assured clear "line-of-sight", as when the "following distance" aft of forward traffic and "steering control" are both adequate. Common examples include when there is no vehicle to be viewed, or when there is a haze or fog that would prevent visualizing a close vehicle in front. This maximum velocity is denoted by the case variable ${\displaystyle V_{ACDA_{s}}}$, the

${\displaystyle \mu }$

, the distance ${\displaystyle d_{ACDA_{s}}}$ is the static ACDA, the constant ${\displaystyle g}$ is the

${\displaystyle t_{prt}}$

See

ACDA: horizontal line-of-sight

The second case describes the relationship of horizontal sight distance on safe speed. It is the maximum speed at which a vehicle can come to a full stop before an object, with speed V_i, can intercept after having emerged and traveled across the horizontal sight distance "d_hsd". Urban and residential areas have horizontal sight distances that tend to be closely obstructed by parked cars, utility poles, street furnishing, fencing, signage, and landscaping, but have slower intercepting speeds of children, pedestrians, backing cars, and domestic animals. These interceptors combined with dense usage results in collisions that are more probable and much more likely to inflict harm to an outside human life. In rural areas, swift-moving spooked wildlife such as deer,^[113] elk, moose, and antelope are more likely to intercept a roadway at over 30 mph (48 km/h). Wildlife will frequently transit across a road before a full stop is necessary, however collisions with large game are foreseeably lethal, and a driver generally has a duty not to harm his or her passengers. The foreseeable intercept speed or defectively designed horizontal sight distance may vary "reasonably" with judicial discretion.

See

ACDA: intersectional setback

This third case regards safe speed around un-signalized intersections where a driver on an uncontrolled through street has a duty to slow down in crossing an intersection and permit controlled drivers to be able pass through the intersection without danger of collision.^[126][147] The driver on the through street must anticipate and hence not approach at an unsafe speed which would prevent another driver from being able to enter while traffic was some distance away, or would be unsafe to a driver who has already established control of the intersection under a prudent acceleration a_i, from a stop at a limit line a distance d_sl away.^[137]

ACDA: following distance

The pedantic fourth case applies when the dynamic ACDA "following distance" (d_ACDAd) is less than the static ACDA "line-of-sight" distance (d_ACDAs). A classic instance of this occurs when, from a visibility perspective, it would be safe to drive much faster were it not for a slower-moving vehicle ahead. As such, the dynamic ACDA is governing the basic speed rule, because in maintaining this distance, one cannot drive at a faster speed than that matching the forward vehicle. The "time gap" t_g or "time cushion" is the time required to travel the dynamic ACDA or "following distance" at the operating speed. Circumstances depending, this cushion might be manifested as a two-second rule or three-second rule.

See Table of 2-second following distances

Critical speed

In the fifth case, critical speed V_cs applies when road curvature is the factor limiting safe speed. A vehicle which exceeds this speed will

See Table of curvatures and critical speeds

Surface control

The bottom case is invoked when the maximum velocity for surface control V_cl is otherwise reached. Steering control is independent from any concept of clear distance ahead. If a vehicle cannot be controlled so as to safely remain within its lane above a certain speed and circumstance, then it is irrelevant how assuredly clear the distance is ahead. Using the example of the previous case, the safe speed on a curve may be such that a driver experiences a lateral acceleration of less than 0.3g despite that the vehicle may not slide until it experiences 0.8g.

Safe speed

Safe speed is the maximum speed permitted by the basic speed law and negligence doctrine. Safe speed is not the same as the 85 percentile operating speed^[151] used by traffic engineers in establishing speed zones.^{[124][134][152][153]} Fog, snow, or ice can create conditions where most people drive too fast, and chain reaction accidents in such conditions are examples of where large groups of drivers collided because they failed to reduce speed for the conditions.^[124][154] The speeds at which most people drive can only be a very rough guide to safe speed,^[124] and an illegal or negligent custom or practice is not in itself excusable.^{[155][81][156][80]} Safe speed approximates the inferred design speed adjusted for environmental alterations and vehicle and person specific factors when V_ACDAs is the limiting factor.^[157] The Solomon curve concept can create an approach-avoidance conflict within the driver who wishes neither to drive faster than is lawful and the conditions allow nor have an unsafe speed discrepancy between other vehicles on the road; it is never legal to go faster than the speed limit, and unilaterally reducing the risk of the latter can lead to a mass crash caused by the former.^[154]

Relationship of posted speed limits to the explicitness of driver care standard

Many people are challenged by the concept of unsafe speed because they find it vague and arbitrary.^[11] It is well known that people instead resolve such challenges by attribute substitution,^[158] which in this case can mean simply emulating the behaviors of others. In accord with the cultural theory of risk, indeed a substantial part of a driver's risk perception comes from comparing their contemplated conduct to the behavior of others; this includes the safeness of a given speed, notwithstanding the actual risk. As a result of this uncorrected vagueness, group behavior can often be in opposition to safe speed and still be governing a hazardous posted speed limit. By federal law, posted speed limits are generally within 5 mph of the 85th-percentile speed of free-flowing traffic.^{[106][134][152][153][159]} Functionality, this amounts to citizens "voting" a street's speed limit with their gas pedal from the influence of groupshift. As people generally follow explicit rules all the time of which they do not agree, it is often simply a jurisdiction's failure in their law to sufficiently quantify and disseminate fair notice of an explicit standard of care, such as the ACDA rule. Most DMV driver manuals teach the practice, but far fewer states explicitly back it up in their actual statutes and law enforcement.^{[1][72][73][74]} If drivers were mindful of the ACDA, the operating speed would by definition not exceed the inferred design speed.^[106][153] In some cases, police focused on driving while "influenced", pull over slower quartile sober night-time drivers moving no faster than they can stop within the radius of their headlights;^[1] this discourages adjusting speed downward from anything but the posted "maximum speed" permitted by law—which is determined as previously described. It is often unsafe or illegal to drive in excess of 40–50 mph at night.^{[116][117][110][160][3][46]}

"Assurance" beyond proximate edge of clear visibility as transference of liability

A general principle in

As it is generally probable and foreseeable that, chance will permit, and at some point there will be an obstruction beyond some driver's line of sight, such an entitlement challenges centuries^[18][19] of precedent in negligence doctrine in addition to posing difficult policy and engineering challenges. It also violates the calculus of negligence^[144] because speed is an inherent factor in vehicular accidents which are a leading cause of priceless life loss^{[165][166][167][168][169][128]} and lawsuits, and the burden of a precautions speed is radically lower than the former.^[169]

The

Even if such criteria are met, the law must also exempt driver liability for maintaining clear distance ahead. In most democracies, such liability for failures of the distance to remain clear beyond line of sight would ultimately be transferred to its taxpayers.[96] This only generally occurs when governments have been tasked by constituents or their courts to take the responsibly to design and maintain roadways that "assure" the distance will be clear beyond the proximate edge of clear visibility. Pressures to make such changes may arise from cultural normalization of deviance and unnecessary risk, misunderstanding the purpose of the road functional classification system, underestimation of increased risk, and reclamation of commute time.^[114]

One of the greatest difficulties created by such an extension of the ACDA is the frequency at which roads reduce their functional classification^[114] unbeknownst to drivers who continue unaware they have lost this extended "assurance" or do not understand the difference. Such nuance in applicable jurisdictions is a prolific source of accidents.^[125] In the United States, there is no explicit road marking promising clear distance beyond line of sight in the Manual on Uniform Traffic Control Devices, although there are signs communicating "limited sight distance", "hill blocks view", "crossroad ahead", and "freeway ends".^[173] A partial solution to this challenge is to remove driver discretion in determining whether the ACDA is extended beyond line of sight, by explicitly designating this law change to certain marked high functional classification roadways having meet strict engineering criteria.^[114]

The ACDA rule is analogous to aviation

Derivation of ACDA 1

Starting with Newton's Second Law of Motion and the Laws of Friction:

${\displaystyle F_{\text{total}}=F_{\text{friction}}+F_{\text{gravity}}\sin \theta }$

${\displaystyle F_{\text{total}}=\mu F_{\text{normal}}+mg\sin \theta }$

${\displaystyle F_{\text{total}}=\mu mg\cos {\theta }+mg\sin \theta }$

Equating the net force to mass times acceleration:

${\displaystyle F_{\text{total}}=ma}$

${\displaystyle \mu mg\cos \theta +mg\sin \theta =ma}$

${\displaystyle a=g(\mu \cos \theta +\sin \theta )}$

Invoking the equations of motion and substituting acceleration:

${\displaystyle d={\frac {v^{2}}{2a}}}$

${\displaystyle d={\frac {v^{2}}{2g(\mu \cos \theta +\sin \theta )}}}$

Small-angle approximation:

${\displaystyle \sin \theta \approx \theta }$

${\displaystyle \cos \theta \approx 1-{\frac {\theta ^{2}}{2}}}$

Substituting the small angle approximations, and exploiting that the product of a small angle squared, in radians, with the friction coefficient, θ²μ, is insignificant (for a steep 20% slope and a good friction coef. of 0.8, this equals (.2)²x0.8≈0.03):

${\displaystyle d\approx {\frac {v^{2}}{2g[\mu (1-{\frac {\theta ^{2}}{2}})+\theta ]}}\approx {\frac {v^{2}}{2g(\mu +\theta )}}}$

Now, the total stopping distance is the sum of the braking and perception-reaction distances:

${\displaystyle d_{\text{total}}=d_{\text{braking}}+d_{\text{perception-reaction}}}$

${\displaystyle d_{\text{total}}\approx {\frac {v^{2}}{2g(\mu +\theta )}}+vt_{pr}}$

Isolating zero as preparation to solve for velocity:

${\displaystyle {\frac {1}{2g(\mu +\theta )}}v^{2}+vt_{prt}-d_{\text{total}}\approx 0}$

Completing the square or invoking the quadratic formula to find the solution:

${\displaystyle v\approx {\sqrt {(\mu +\theta )^{2}g^{2}t_{prt}^{2}+2(\mu +\theta )gd_{\text{total}}}}-(\mu +\theta )gt_{prt}}$

Use

e

" instead of an angle θ in radians:

${\displaystyle \theta \approx \tan(\theta )={\frac {\%{\text{grade}}}{100}}}$

Substituting the angle as described produces the form of the formula of case 1 ():

${\displaystyle V_{BSL1}\approx {\sqrt {(\mu +e)^{2}g^{2}t_{prt}^{2}+2(\mu +e)gd_{ACDA}}}-(\mu +e)gt_{prt}}$

The Basic Speed Law constrains the assured clear distance ahead to the total stopping distance, and the small angle value of

superelevation

"e."

Many roadways are level, in which case the small angle approximations or superelevation may be dropped altogether:

${\displaystyle V_{BSL1}={\sqrt {\mu ^{2}g^{2}t_{prt}^{2}+2\mu gd_{ACDA}}}-\mu gt_{prt}}$

This model ignores the effects of

level ground model with most of those effects here or read about the automobile drag coefficient

.

Case 4: Safe speed as a function of following distance

Case 5: Safe speed as a function of critical speed

Derivation of ACDA 5

Starting with Newton's Laws of Motion, the Laws of Friction, and Centripetal force:

${\displaystyle F_{\text{centripetal}}\cos {\theta }=F_{\text{friction}}+F_{\text{gravity}}\sin \theta }$

Substituting formulas for Centripetal force, frictional force, and gravitational force:

${\displaystyle m{\frac {v^{2}}{r}}\cos \theta =\mu F_{\text{normal}}+mg\sin \theta }$

The normal force is equal and opposite to the sum of the gravitational and centripetal components:

${\displaystyle m{\frac {v^{2}}{r}}\cos \theta =\mu (mg\cos {\theta }+m{\frac {v^{2}}{r}}\sin \theta )+mg\sin \theta }$

Isolate ${\displaystyle v}$ terms:

${\displaystyle {\frac {v^{2}}{r}}\cos \theta -\mu {\frac {v^{2}}{r}}\sin \theta =g(\mu \cos \theta +\sin \theta )}$

Then solve for ${\displaystyle v}$:

${\displaystyle v^{2}(\cos \theta -\mu \sin \theta )=gr(\mu \cos \theta +\sin \theta )}$

To obtain:

${\displaystyle v={\sqrt {\frac {gr(\mu \cos \theta +\sin \theta )}{\cos \theta -\mu \sin \theta }}}}$

This is the full solution, however most corners are banked at less than 15 degrees (≈28% grade), so in such conditions, a fieldable small angle approximation may be used.

Substituting small-angle approximations sin θ ≈ θ, cos ≈ 1 − θ²/2:

${\displaystyle v\approx {\sqrt {\frac {gr[\mu (1-{\frac {\theta ^{2}}{2}})+\theta ]}{1-{\frac {\theta ^{2}}{2}}-\mu \theta }}}}$

Exploit that a small angle squared, in radians, is insignificant by substituting θ²≈0 which obtains the formula used in case 5 (also tan θ≈e):

${\displaystyle v\approx {\sqrt {\frac {gr(\mu +\theta )}{1-\mu \theta }}}\approx {\sqrt {\frac {gr(\mu +e)}{1-\mu e}}}}$

Seconds of distance to stop rule

Tables of reference constants and safe speeds

Reference constants

Table of perception-reaction times

Table of tire-roadway friction coefficients

Table of acceleration values

Table of intercept values

Table of tire speed ratings

Safe speeds

Table of ACDA: forward line-of-sight

Table of ACDA: horizontal line-of-sight

Table of detection thresholds

See also

• Advisory speed limit
• Assumption of risk
• Basic speed rule
• Braking distance
• Following distance
• Calculus of negligence
• Duty of care
• Effects of insufficient sight distance
• Heinrich's Law
• Illusory superiority
• International Regulations for Preventing Collisions at Sea—Part B, Section I, Rule 6: Safe speed
• Road traffic safety
• Standard of care
• The man on the Clapham omnibus
• Two-second rule
• Visual flight rules
• Volenti non fit injuria

Notes