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Whether or not to run in the rain
Abstract
The problem of choosing an optimal strategy for moving in the rain has attracted considerable attention among physicists and other scientists. Taking a novel approach, this paper shows, by studying simple shaped bodies, that the answer depends on the shape and orientation of the moving body and on wind direction and intensity. For different body shapes, the best strategy may be different: in some cases, it is best to run as fast as possible, while in some others there is an optimal speed.
... Analyzing an object with a certain velocity under rain has been investigated by physicists and other scientists. Bocci (2012) has proven that the amount of water hitting an object under rain depends on its shape, its orientation, wind direction and rain intensity. The main purpose of the car speed simulator is to investigate this effect in the laboratory. ...
... Considering the direction of the moving plane (car) as the x axis and the direction of the falling rain drops as the z axis, the windshield angle affects the projected area corresponding to both axes. Bocci (2012) introduced v = (v x , v y , v z ) as the rain velocity where the vertical component, v z , depends on the drop size. He called ρ the ratio between the mass of water drops that are found within a given volume and the volume itself. ...
... Car speed is one of the important influential factors for the estimation of rainfall by moving cars. Theoretically, there is a positive linear relationship between the velocity of an object with a plane surface under rain and the water mass hitting the object (Bocci, 2012). This means when a car moves with higher speed the rainfall intensity measured by car sensors would be overestimated compared to a stationary ground reference value, linearly proportional to its speed. ...
The spatial assessment of short time-step precipitation is a challenging task. Low density of observation networks, as well as the bias in radar rainfall estimation motivated the new idea of exploiting cars as moving rain gauges with windshield wipers or optical sensors as measurement devices. In a preliminary study, this idea has been tested with computer experiments (Haberlandt and Sester, 2010). The results have shown that a high number of possibly inaccurate measurement devices (moving cars) provide more reliable areal rainfall estimations than a lower number of precise measurement devices (stationary gauges). Instead of assuming a relationship between wiper frequency ( W ) and rainfall intensity ( R ) with an arbitrary error, the main objective of this study is to derive valid W - R relationships between sensor readings and rainfall intensity by laboratory experiments. Sensor readings involve the wiper speed, as well as optical sensors which can be placed on cars and are usually made for automating wiper activities. A rain simulator with the capability of producing a wide range of rainfall intensities is designed and constructed. The wiper speed and two optical sensors are used in the laboratory to measure rainfall intensities, and compare it with tipping bucket readings as reference. Furthermore, the effect of the car speed on the estimation of rainfall using a car speed simulator device is investigated. The results show that the sensor readings, which are observed from manual wiper speed adjustment according to the front visibility, can be considered as a strong indicator for rainfall intensity, while the automatic wiper adjustment show weaker performance. Also the sensor readings from optical sensors showed promising results toward measuring rainfall rate. It is observed that the car speed has a significant effect on the rainfall measurement. This effect is highly dependent on the rain type as well as the windshield angle.
... With an angle prescribed along the direction of travel, potentially different recommendations may be made. With a component of the wind at a person's back (or motion upwind), there may be an optimum speed to run, which corresponds to the wind speed (see for example, [4] and [16]). However, Bailey [11] also showed that the shape can be a factor with this consideration and that an optimum speed may or may not correspond to the wind speed based on the body shape. ...
... However, Bailey [11] also showed that the shape can be a factor with this consideration and that an optimum speed may or may not correspond to the wind speed based on the body shape. Other authors [12,15,16] also developed analyses based on alternative shape models, including cylindrical and ellipsoidal shapes. ...
... While most analyses involve the assumption of a parallelepiped shape for the person, a few studies also considered cylindrical and ellipsoidal shapes (see for example, [12]- [16]). Shape considerations seem to expand the range of conclusions as well. ...
The age-old question of whether to run or walk in the rain still raises interest because of its practical relevance. A number of published studies have been carried out to address this question. These studies showed that there is no trivial answer and that different factors, including the rain conditions (rate and angle), the walking/running speeds and even the geometry used for analysis and the shape of the person matter. In the present paper, we present an analysis of the rate and amount of rain accumulation on a person walking/running through the rain using the Reynolds transport theorem (RTT) and its implementation for mass conservation. A new twist to earlier analyses is added, which involves the usage of a simplified model for an umbrella. The present work illustrates the use of RTT to establish the observations made using different analyses as well as demonstrates the RTT problem with this new twist.
... The rain angle of a vertically falling droplet is influenced by the horizontal interference of air flow [9]. In other words, the droplets do not strike normal to the ground surface in the presence of wind. ...
... This model was used to derive a safe overtaking distance dependent on overtaking speed and further vessel characteristics like the radius of turn and response time. An investigation of whether an optimum speed exists to minimize the amount of rain falling onto a moving body found, even for simple shaped bodies like cylinders or parallelepipeds, that the solution depended on rain/wind direction and the shape of the body [26]. Raindrops were represented as a flux, so the actual size of the drops was not taken into account and the method was applied to bodies moving with constant velocity on a straight line. ...
The mathematical problem of establishing a collision probability distribution is often not trivial. The shape and motion of the animal as well as of the the device must be evaluated in a four-dimensional space (3D motion over time). Earlier work on wind and tidal turbines was limited to a simplified two-dimensional representation, which cannot be applied to many new structures. We present a numerical algorithm to obtain such probability distributions using transient, three-dimensional numerical simulations. The method is demonstrated using a sub-surface tidal kite as an example. Necessary pre- and post-processing of the data created by the model is explained, numerical details and potential issues and limitations in the application of resulting probability distributions are highlighted.
... A familiar problem treats how wet a person walking in rain becomes as they travel a given horizontal distance at different speeds [1][2][3]. As a variation on this scenario, consider a triangular cart that can roll along a horizontal surface under the impulse of raindrops (or hail) falling vertically at terminal speed u that bounce elastically [4,5] off the cart's two surfaces sketched in figure 1. ...
A frictionless cart in the shape of a right triangle (with the vertical side forward) is elastically impacted by vertically falling raindrops. The speed of the cart as a function of time can be analytically deduced as an exercise in the use of trigonometric and hyperbolic functions. A characteristic time defines the approach to a terminal speed which is a sizeable fraction of the speed of the rain. The treatment is accessible to a student in a calculus-based mechanics course.
... The two most striking examples in this specific case were "What is the taste of rain?" and "Should I walk or run under the rain to get less wet?". The latter was especially fun, and after a little research it turns out that almost ten papers based on numerical or actual experiments can be found on this topic in the scientific literature (see Bocci, 2012 for a recent study with many references within). It appears that, in general, one should run as fast as possible when it is raining, but in some windy conditions or for certain body shapes, there exists an optimal velocity. ...
Research projects now rely on an array of different channels to increase impact, including high-level scientific output, tools, and equipment, but also communication, outreach, and educational activities. This paper focuses on education for children aged 5–12 years and presents activities that aim to help them (and their teachers) grasp some of the complex underlying issues in environmental science. More generally, it helps children to become familiarized with science and scientists, with the aim to enhance scientific culture and promote careers in this field. The activities developed are focused on rainfall: (a) designing and using a disdrometer to observe the variety of drop sizes; (b) careful recording of successive dry and rainy days and reproducing patterns using a simple model based on fractal random multiplicative cascades; and (c) collaboratively writing a children's book about rainfall. These activities are discussed in the context of current state-of-the-art pedagogical practices and goals set by project funders, especially in a European Union framework.
... Eine aktuelle Veröffentlichung, die den Seitenwind mit berücksichtigt, kommt zu dem Ergebnis, dass die optimale Geschwindigkeit sich von der Horizontal- geschwindigkeit des Regens unterscheiden kann [6]. Auch hier wird gezeigt, dass die Existenz eines Mi- nimums einerseits vom Verhältnis Höhe / Radius eines Körpers, andererseits aber auch vom Verhält- nis der Geschwindigkeitskomponenten des Regens v horiz /v vert abhängt. ...
Die Frage, ob man bei Regen lieber langsam gehen oder schnell laufen sollte, um möglichst tro-cken zu bleiben, ist schon in vielen theoretischen und praktischen Arbeiten behandelt worden. In-teressanterweise haben selbst kleine Änderungen in der mathematischen Modellierung des Prob-lems oft signifikante Auswirkungen auf die Ergebnisse, die sich nicht nur quantitativ, sondern auch qualitativ ändern können. Der Artikel gibt einen Überblick über bisherige Experimente und Berechnungen sowie über die Unterschiede in den verschiedenen theoretischen Modellen.
Mit dieser einfachen Fragestellung, die aber stark von den physikalischen Parametern der Rech-nung abhängt, können Schüler und Studierende selbst anhand geometrischer Überlegungen eigene Formeln entwickeln und überprüfen, wie stabil das Ergebnis, das sich leicht beispielsweise mittels Microsoft Excel darstellen lässt, gegenüber welchen Veränderungen der physikalischen und geo-metrischen Randbedingungen ist.
It is a common experience that raindrops falling vertically appear to fall at an angle to a moving person. When trying to describe the sheltered area provided by an umbrella from the viewpoints of both moving and stationary observers, at first glance it may appear that the descriptions for the sheltered area in these two frames are not identical. It is shown as well as illustrated by simulation that the sheltered areas are indeed identical in both these frames as expected. The physics behind this is explained and in the process confirming distances, angles, and consequently areas, remain invariant under a Galilean transformation. The detailed treatment of the problem given in this paper may help undergraduate students gain a robust understanding of the important concepts of frame of reference and Galilean transformation.
Areal rainfall information is one of the most important inputs to hydrological models. This paper presents some theoretical considerations and initial results on the idea of using a geosensor network of cars as a data source for areal rainfall estimations. The types of car sensors and different calibration schemes for the rainfall estimation functions (W-R functions) in the cars are presented. A special focus is given to the decentralized online calibration of these functions in the network by communicating measurements between measuring units. This would allow the dynamic adaptation of the functions to different situations such as different drivers, the current car environment or the current wind speed and direction. Then, results from laboratory and field experiments are presented.
Areal rainfall estimation is still one of the concerns in hydrological
analyses. Low density of the conventional rainfall measurement devices
as well as the errors in radar data developed the new idea of using
moving cars, called raincars, as a possible new source for measuring
rainfall. This idea is easily technically feasible if the cars are
provided with GPS and a small memory chip for recording the coordinates,
car speed and data from the sensors, either for the frequency
measurement of the wipers or the optical sensors on cars. According to
the modeling study, which is done on the Bode catchment in Germany, a
high number of possibly inaccurate sensors, raincars, provide more
reliable areal rainfall estimation than a lower number of highly
accurate, stationary sensors. In this study, data for the stationary
gauges and the cars are extracted from the radar data. A valid
relationship between wiper frequency and rainfall with a known error is
assumed where the radar data is considered as the reference. Areal
precipitation is estimated by different interpolation techniques,
ordinary kriging for the stationary stations and indicator kriging for
the cars. The results are then compared and evaluated with the
reference, radar. After proving the feasibility of the hypothesis in the
modeling study, field and laboratory experiment have been arranged. A
certain number of cars has been equipped with sensors and in the
laboratory, to produce the rainfall as close as possible to nature,
sprinkler irrigation system has been designed for producing different
rain intensities, from 1 mm/hr to 55 mm/hr. Here, we can develop an
empirical approach for the relationship between the wiper frequency and
rainfall intensity as well as for the optical sensors on the cars under
different rainfall intensities.
An exercise which relates particle scattering and the calculation of cross-sections to answer the following question--"Do you get wetter by walking or running through the rain?"--is described. The calculations used to answer the question are provided. (KR)
Whether it is better to walk or run through a rain shower is a question often posed by adult and child alike. The answer to this question requires careful physical analysis and provides an instructive, even illuminating exercise for high school as well as undergraduate introductory physics classes. In this paper, we will derive a rule for the optimal travel speed which minimizes the number of rainstrikes on a given surface element over a given course. We shall also investigate the speed versus intensity relationship. Methods of extending these results to include rainfalls with horizontal velocity relative to the travel path and for surfaces of arbitrary geometry are presented in Sec. VI.
A problem strongly debated between students (and not only students!) is discussed: when one gets caught in a storm without an umbrella, is it worth running as fast as possible to get less wet?.
The question whether to walk slowly or to run when it starts raining in order to stay as dry as possible has been considered for many years—and with different results, depending on the assumptions made and the mathematical descriptions for the situation. Because of the practical meaning for real life and the inconsistent results depending on the chosen parameters, this problem is well suited to undergraduate students learning to decide which parameters are important and choosing reasonable values to describe a physical problem. Dealing with physical parameters is still useful at university level, as students do not always recognize the connection between pure numbers and their qualitative and quantitative influence on a physical problem. This paper presents an intuitive approach which offers the additional advantage of being more detailed, allowing for more parameters to be tested than the simple models proposed in most other publications.
HorvàthHorvàth´ Horvàth´A and Pitharoulis I 1995 Raindrops keep falling on my head Weather 50
- J J Holden
- S Belcher
Holden J J, Belcher S E, HorvàthHorvàth´ Horvàth´A and Pitharoulis I 1995 Raindrops keep falling on my head Weather 50 367-70
On running in the rain Coll
- H Bailey
Bailey H 2002 On running in the rain Coll. Math. J. 33 88-92