Speed sounds like a simple thing to measure until you try. Ask “how fast is traffic moving on this road?” and you immediately face a choice — do you mean at a particular point or over a length? Do you average the speeds of vehicles, or the time they take? Those choices give different numbers, and getting them right is what this topic is about.
This post covers spot speed, the two kinds of mean speed with their formulas, and the percentile speeds used in design and regulation.
Why Several Definitions of Speed Exist
Speeds of different vehicles vary with respect to time and space. To describe that variation properly, several types of speed have to be defined.
1. Spot Speed
Spot speed is the instantaneous speed of a vehicle at a specified location or instant.
What Spot Speed Is Needed to Design
- Horizontal and vertical curves
- Location and size of signs
- Design of signals
- Accident analysis
How It Is Measured
- Enoscope
- Pressure contact tubes
- Loop detector
- Doppler radar
2. Average Speed
Average speed is the average of the spot speeds of all vehicles passing a given point on the road.
There are two types of mean or average speed, and the difference between them is the single most examined point in this topic:
- Time mean speed
- Space mean speed
Time Mean Speed (Vt)
- It is the arithmetic mean of the speeds of vehicles passing a point on a highway during an interval of time.
- It represents the speed distribution of vehicles at a point on the roadway.
Vt = ( Σ Vi ) / n
| Symbol | Meaning | Unit |
|---|---|---|
| Vt | Time mean speed | kmph |
| Vi | Observed instantaneous speed of the i-th vehicle | kmph |
| n | Number of vehicles observed | — |
Space Mean Speed (Vs)
- It is the average speed of vehicles over a certain road length at any time.
- It is obtained by dividing the total distance travelled by two or more vehicles on a section of highway by the total time required by those vehicles to travel that distance.
- It is the harmonic mean of the speeds of vehicles.
- It is the speed used for flow–density relationships, that is, in traffic flow studies.
Vs = nL / Σti = n / Σ(1/ui)
where L is the length of the section, ti is the time taken by the i-th vehicle, and ui is the speed of the i-th vehicle.
Time Mean versus Space Mean: The Key Comparison
| Time Mean Speed | Space Mean Speed | |
|---|---|---|
| Type of average | Arithmetic mean | Harmonic mean |
| Measured over | A point, during an interval of time | A length of road, at an instant |
| Represents | Speed distribution at a point | Average speed over a section |
| Used in | Spot speed analysis | Flow–density relationships and traffic flow studies |
The reason for the harmonic mean is worth understanding. A slow vehicle spends more time inside the study section than a fast one, so it influences the section’s average more heavily. The harmonic mean gives that extra weight automatically, which is why space mean speed is the correct speed for flow calculations.
One consequence follows directly and is a common objective question: time mean speed is always greater than or equal to space mean speed.
Spot Speed Study: Uses
Six uses are recognised:
- In planning traffic control and traffic regulations
- In geometric design — for redesigning existing highways or deciding the design speed for new facilities
- In accident studies
- To calculate traffic capacity
- To decide speed trends
- To compare diverse types of drivers and vehicles under specified conditions
Factors Affecting Spot Speed
Road-related factors:
- Pavement width
- Curve
- Sight distance
- Gradient
- Pavement unevenness
- Intersections
- Roadside developments
Other factors:
- Environmental conditions
- Enforcement
- Traffic conditions
- Driver
- Vehicle
- Motive of travel
An Important Limitation
Spot speed studies cannot be used to find density, because measurements are taken at one point only.
Remember: density = number of vehicles per kilometre.
Density is defined over a length of road. A measurement at a single point contains no information about length, so density simply cannot be extracted from it. This limitation is precisely why speed and delay studies exist, and it is a favourite examination point.
Presentation of Spot Speed Data
a) Average Speed of Vehicles
From the spot speed data of selected samples, frequency distribution tables are prepared for various speed ranges and the number of vehicles in each range. This table gives the general pattern of speed distribution, and from it both space mean speed and time mean speed are calculated.
b) Cumulative Speed of Vehicles
A graph is plotted between the average value of each speed group and the cumulative percentage of vehicles travelling at or below different speeds.
From this cumulative curve, three important percentile speeds are read off.
85th Percentile Speed — the Safe Speed Limit
- Only 15 percent of vehicles exceed this speed.
- It is considered the safe limit for the zone.
- All drivers exceeding the 85th percentile speed are considered faster than the safe speed.
The logic here is that the great majority of drivers choose a sensible speed for the conditions. Rather than imposing a limit from outside, the 85th percentile lets the traffic itself indicate what is reasonable, and treats the fastest 15 percent as the outliers.
98th Percentile Speed — for Geometric Design
For the purpose of highway geometric design, the 98th percentile speed is considered.
Design uses a higher percentile than regulation does, and for good reason. A speed limit is a rule that some will break; geometry is a physical fact that must hold even for the fast minority. A curve designed only for the 85th percentile would be unsafe for the 15 percent travelling faster.
15th Percentile Speed — the Lower Limit
- Taken as the lower speed limit.
- It is derived to prohibit slow moving vehicles so as to decrease delay and congestion.
- The purpose is segregation of fast moving vehicles from slow moving ones.
A very slow vehicle in a fast stream is a hazard, not a caution. It forces others to overtake, and overtaking is where crashes happen.
c) Modal Average
A speed distribution curve is plotted with the speed of vehicles, or the average value of each speed group, on the X-axis, and the percentage of vehicles in that group on the Y-axis.
This curve shows the speed at which the greatest proportion of vehicles moves, and that speed is called the modal speed.
Example: if the peak of the distribution curve occurs at 47 km/hr, then the modal speed is 47 km/hr, because the largest percentage of vehicles is moving at that speed.
The Three Percentile Speeds Together
| Percentile | Meaning | Used For |
|---|---|---|
| 15th | 85 % of vehicles exceed it | Lower speed limit, segregating slow traffic |
| 85th | Only 15 % of vehicles exceed it | Safe speed limit for the zone |
| 98th | Only 2 % of vehicles exceed it | Highway geometric design |
Formula Summary
| Quantity | Expression |
|---|---|
| Time mean speed | Vt = ΣVi / n (arithmetic mean) |
| Space mean speed | Vs = nL / Σti = n / Σ(1/ui) (harmonic mean) |
| Density | Number of vehicles per kilometre |
Quick Revision Notes
- Spot speed = instantaneous speed at a specified location or instant.
- Measured using Enoscope, pressure contact tubes, loop detector and Doppler radar.
- Spot speed is needed for horizontal and vertical curves, sign location and size, signal design and accident analysis.
- Time mean speed = arithmetic mean, taken at a point over an interval of time.
- Space mean speed = harmonic mean, taken over a length of road.
- Space mean speed is used in flow–density relationships.
- Time mean speed is always greater than or equal to space mean speed.
- Spot speed studies cannot give density, since they observe one point only.
- 85th percentile = safe speed limit; 98th percentile = geometric design; 15th percentile = lower speed limit.
- Modal speed = the speed at which the greatest proportion of vehicles moves, read from the speed distribution curve.
Mistakes Students Commonly Make
- Using the arithmetic mean for space mean speed. It is the harmonic mean.
- Using time mean speed in flow–density relationships. Those require space mean speed.
- Using the 85th percentile for geometric design. Design uses the 98th; the 85th is for speed limits.
- Thinking the 15th percentile is a safety maximum. It is a minimum, aimed at slow vehicles.
- Saying the 85th percentile means 85 percent of vehicles exceed it. Only 15 percent do.
- Trying to obtain density from spot speed data.
- Confusing modal speed with mean speed. The mode is the most common speed, not the average.
Conclusion
Speed studies teach a lesson that runs through all of traffic engineering — the same physical situation yields different numbers depending on how you choose to measure it. Time mean speed and space mean speed both describe the same traffic and both are correct, but they answer different questions and are used in different places. Add the three percentile speeds, each serving a distinct regulatory or design purpose, and you have a complete toolkit for describing how fast traffic actually moves.
Frequently Asked Questions
What is spot speed?
The instantaneous speed of a vehicle at a specified location or instant.
How is spot speed measured?
Using an Enoscope, pressure contact tubes, a loop detector or Doppler radar.
What is time mean speed?
The arithmetic mean of the speeds of vehicles passing a point on a highway during an interval of time, given by Vt = ΣVi/n.
What is space mean speed?
The average speed of vehicles over a length of road, obtained by dividing the total distance travelled by the total time taken. It is the harmonic mean of the vehicle speeds.
Which mean speed is used in traffic flow studies?
Space mean speed, because it is the speed used for flow–density relationships.
Why is space mean speed a harmonic mean?
Because slower vehicles spend longer within the study section and therefore influence the section average more. The harmonic mean weights them accordingly.
Why can spot speed studies not measure density?
Because density is the number of vehicles per kilometre, which requires observation over a length. Spot speed measurements are taken at a single point.
What is the 85th percentile speed used for?
It is taken as the safe speed limit for the zone. Only 15 percent of vehicles exceed it, and those drivers are considered to be travelling faster than the safe speed.
Which percentile speed is used for geometric design?
The 98th percentile speed.
What is the 15th percentile speed for?
It is taken as the lower speed limit, used to prohibit slow moving vehicles so as to reduce delay and congestion and to segregate fast from slow traffic.
What is modal speed?
The speed at which the greatest proportion of vehicles moves, identified from the peak of the speed distribution curve.