Intercontinental Ballistic Missiles

During the last months we heard (and read) a lot of news about ballistic missiles and potential threads of North Korea testing Intercontinental Ballistic Missiles (ICBM). But what is an intercontinental ballistic missile and why does it pose such a threat?
First, it is important to understand what a ballistic missile is. Basically, there are 2 types of missiles: ballistic missile and cruise missiles (will be explained in another post).
A ballistic missile is a missile that follows a ballistic trajectory; that is, the path that any given thrown object (or projectile) without propulsion would take under the action of gravity. A theoretical perfect projectile trajectory only considers gravity but real projectiles also consider additional forces such as friction due to aerodynamic drag (Figure 1).
Fig 1. Ballistic trajectory

The flight of a ballistic missile has 3 phases: A first phase is a powered flight (launching); in long range missile the launching requires enough force so that the missile escapes the atmosphere. The second phase which is the longest phase is the free flight (a ballistic projectile). Usually, this second phase is outside of the atmosphere; hence, the missile has less friction. The third phase is the re-entry phase.
Ballistic missiles can be divided in four groups based on their range (Figure 2):
Short range ballistic missile. This missiles have a range between 300 km to 1000 km and may reach their target in less than 10 min.
Medium range. This missiles have a range between 1000 km and 3500 km and may reach their target in between 10 min to 15 min.
Intermediate range. This missiles have a range between 3500 km and 5000 km and may reach their target in between 15 min to 20 min.
Intercontinental range. This missiles have a range greater than 5000 km (up to 13000 km) and may reach their target in between 20 min to 30 min.
Fig 2. Range of ballistic missiles if launched from North Korea

The thread
ICBM are big threat to world's peace because of 2 factors: their range and short time to reach their target.
Range. Ballistic missiles flying above the atmosphere have a range much longer than any other missile. ICBM may easily reach target distances about 10000 km.  That is, a missile launched from North Korea may reach any European capital, any Asian city, Australia or even some major American cities such as Seattle, Los Angeles, Las Vegas or Houston.
Time to target. ICBM may reach velocities about 5 km/s and may require only 30 min to travel up to 10000 km. That is, any of the previously mentioned cities could be destroyed in just 30 min after the launch is detected. With such a short time, there would be no option to evacuate or to appropriate shelter. Thus, ICBM are lethal.

Fig 3. Ballistic missiles

This short introduction to ICBM clearly illustrates their potential as destructive lethal mass destruction weapons. Although America is developing-testing a missile defensive system, ICBM are still a threat 

Online hydraulic design and calculations

The advance in mobile apps and internet accessibility changed the way we socialize and the way we work: Sharing information, instant communications, cloud computing and online calculations are just few examples of the internet in our daily life. One advantage of mobile apps and online calculations is that they liberate us from the desktop and allows us performing engineering calculations on site, as soon as we need or as soon as we collect new data.

Fig1. Welcome screen OTOSHEE

Some years ago, I created a website for performing some calculation that I used quite often. Over the years I’ve been including new equations, but the interface was not so friendly. I decided to improve the interface and make it friendlier, so that it can be used by others. Try the online hydraulic design website.

Fig 2. Screen OTOSHEE

Available options

The web site contains sections for:
  • Time of concentration. 4 time of concentration equation are available.
  • Rip rap. Rip rap sizing for piers and abutments.
  • Weirs & gutters. Discharge estimation for weirs and gutters.
  • Pipes. Head losses and minimum pipe diameter estimation.
  • Scour. Hydraulic scour estimation for groynes, weirs and pipes.
  • IDF precipitation. An online interactive GIS map with IDF equation for different locations.

Fig 3. IDF precipitation screen

Precipitation intensity for highway & bridge drainage design

Drainage projects usually consider a precipitation intensity based on the time of concentration and the return period. However, when designing drainage systems for bridges and highways it is important to verify the compatibility between the precipitation intensity and the driver's safety. Thus, two additional criterion should be considered: Hydroplaning and visibility.

Hydroplaning is the situation when when a layer of water is built between the wheels of a vehicle and the road surface. Hydroplaning leads to a loss of traction. The driver  of the vehicle looses control and the vehicle begins to slide. The hydroplaning of a vehicle is a function of the speed, the water depth and the inflation pressure of the wheels.

Figure 1. Hydroplaning concept (Source: Tirebuyer)

The hydroplaning based intensity is a new approach to drainage design. It seeks that rainfall that is just sufficient to cause a water depth of sheet flow at the edge of the traveled way that will cause hydroplaning. The design concept is that removal and control of flooding, caused by rainfall in excess of rainfall that will cause hydroplaning, is overdesign from a vehicle safety standpoint.

The limit speed is defined by the standards of the highways or bridge deck. Then, the speed that initiates hydroplaning is used for defining the water depth D when hydroplaning occurs. The most popular studies about hydroplaning speed are the studies performed by NASA and Gallaway et al., (1979). Then, it is assumed that water flows in sheet with depth D across the surface to the edge of the gutter. Combining the depth D with the rational formula and the Manning equation it is possible to define the hydroplaning design rainfall intensity.

Figure 2. Hydroplaning speed equation reported by Gallawat et al., (1979).

The rainfall and the windshield wipers reduce the visibility of the driver. Such visibility reduction also reduces the safe stopping distance.

Figure 3. Driver visibility during rain (Source: Earth magazine)

The visibility design concept is that drainage removal or control of flooding caused by rain in excess of that rain, which will cause driver vision impairment, is overdesign from a vehicle safety standpoint (more drainage capacity than required).

The safe stopping distance is a function of the vehicle speed and the mechanical characteristics of the vehicle (break time and deceleration). Thus, this design criterion uses the rain intensity that allows a visibility equal to the safe stopping distance. Several studies analyzed the visibility considering the effect of different rain intensities and windshield wipers. One of the first methods for estimating the driver's visibility under different rainfall intensities and vehicle speeds is based on the experiments from Ivey et al., (1975).

We can see that there is no single method for estimating the rainfall intensity. Thus, the selection of the highway-bridge rainfall intensity is a multi-criteria process. It is suggested to consider all the criterion; the two criterion from this post and the traditional IDF - rational criterion. Then, engineering criterion should decide the optimum one.

If you require advice for design of highway/bridge drainage or doubts about the rainfall intensity, feel free to contact us.

Figure 4. Driver visibility suggested by Ivey et al., (1975)