A.G. Ibrahim

Department of Physics, Federal University of Technology, Minna.



The work employs the fundamental principle of elasticity in putting together an apparatus comprising a network of both spiral and helical springs attached to an aluminium frame and embodied in a padded cotton fabric. Hookes law provided the theoretical guide for the choice of spring constant for both spiral and helical spring as 23.33Nm-1 and 7.78 Nm-1 respectively. A prototype was designed using the Sweet Orange (citrus cinensis) as a case study. At the height of 5.9m ± 1m, the spiral and helical springs effectively played the role of cushioning effect and rebound prevention respectively.


Keywords: Bruise, prevention, fruits, Hooke’s law, spiral and helical springs



The concept of fruit bruises and its consequences  include softening, change in colour, change in taste and in certain cases injury on affected portions with the overall effect of a decline in available fruits (Ibrahim, 2006). This concern led to a separate work in which a bruise detection apparatus was designed and constructed using state of the art electronic components. The said device, a fruit transducer, provides a yardstick for the measurement of bruises inflicted on fruits especially during harvesting (Ibrahim eta al, 2006) and (Ibrahim, 2009a). Testing was carried out using fruits of interest at various heights. The bruise data collected was analyzed and a bruise prediction model arrived at (Ibrahim, 2009b). Beyond detection and prediction of fruit bruises is an important phenomenon, which is, bruise prevention. In this work, a bruise prevention apparatus was designed to help save the disturbing phenomenon of fruit bruises.


The basic principle applied here is the fundamental principle of elasticity as put forward by Robert Hooke and generally known as Hooke’s law. The law is stated mathematically as;



Where   is the spring force and  the displacement. The minus sign indicates that the spring force is always opposite in direction from the displacement. The constant  is called the spring constant (force or stiffness constant) and is a measure of the stiffness of the spring (Halliday etaal, 2006).

In this work, an arrangement of basically springs of appropriate spring constants were systematically put together in order to help overcome bruises inflicted on fruits during harvesting. These springs are, the spiral spring, to serve as compression spring and the helical spring to serve as expansion spring.

Equation (1) can be rewritten as,


Where  is the average mass of the fruit of interest and  is the acceleration of free fall taken to be 10ms-1.

Let s be the spring constant of the spiral spring and h be the spring constant of the helical spring. Therefore, equation (2) can be written for the spiral and the helical spring respectively as,

                                                                   sx                                                                   (3)

                                                                    hx                                                                  (4)

The design is such that the displacement (compression in case of spiral spring and extension in case of helical spring) under the action of a falling fruit is the same. Secondly, the points at which they experience a restoring force after being compressed (or extended) are the same. Therefore, we can combine equation (2) to (4) as,

sx = hx                                                           (5)

This implies,

sx = hx                                                                 (6)

The primary function of the helical spring is rebound prevention. It does this by pulling the spiral spring back in place before reaching the point at which it releases its stored potential energy as a restoration force. This happens when the spiral spring is compressed freely to it maximum point and usually results in throwing the fruit back into air. To do this, the helical spring is made stiffer than the spiral spring. This is done by using only three of the four helical springs in the design calculation. The fourth will be added physically to ensure this point is not reached. It follows therefore, that (6) can now be written as,

                                                                    s = h                                                                    (7)

To select the value of s, recall equation (3),


                                                                 s =                                                       (8)

Sweet Orange (citrus cenensis)  was used as a case study, being the most cultivated fruit in Benue State (Akinboro, 1988). With an average mass of 140g, acceleration of free fall of 10ms-1, the maximum allowable compression x of the spiral spring before the pulling action of the helical springs was chosen to be 6cm. Therefore, the spring constant of the spiral spring was worked out to be 23.33Nm-1. It also follows from (7) that the spring constant of the helical spring h is 7.78 Nm-1. Table 1. Shows the specification of the springs used.


Table 1. Specifications of spiral and helical springs


Spiral spring

Helical spring

Material of spring



Length of  spring



Spring Constant

23.33 Nm-1

7.78 Nm-1





Cushioning Effect

Rebound Prevention


The permissible height h, which a fruit can fall from for optimal performance of the apparatus was also obtained using the expression for the work done. The work done, E on the spiral spring by the falling fruit is given as;


Just before the fruit of mass M at a height h begins to fall with the acceleration of free fall g, (9) can be rewritten as,



This height was calculated to be 5.9m. Experiments have shown efficiency within limit of ±1m. This also being within range of most improved varieties of Sweet Orange . At height , a fruit of mass , compresses the spiral spring of spring constant by and also extends the helical spring of spring constant h by same distance , thereby activating the cushioning effect and the rebound prevention effect of the spiral and helical springs respectively.

 Both springs were systematically attached together and to an aluminium metal frame. A prototype of this apparatus was made using aluminium strip of 1.5cm wide and 0.2cm thick. It has an advantage of being light in weight. The frame is 3m x 2m in dimension with cross rods at 33cm apart along the entire length and breadth. Summing to nine crosses and six crosses for the length and breadth respectively. The spiral springs were attached at the points of intersection of the cross rods. A total of fifty four were used with each surrounded by four neighbours except those at the edges which has three. The helical springs were used to fasten each spiral spring to its neighbours, those at the edges were fastened to another frame held at same height with the network with the aid of supportive rods. The schematic diagram of the apparatus is shown in figure 1.




Cross rod


Spiral spring


Aluminum frame


Helical spring








Fig1. Schematic diagram of the apparatus


The set up above constitute a set. Two or more sets can be put together in order to cover a wider area should the need arises.

Casing: The embodiment of the spiral network and its aluminium frame is a cotton fabric which has 2mm foam as underlay. This safeguard the fruit from injury it might sustain incase it lands on the edges of the springs or frame. It also provides a medium soft enough for the fruit to enjoy the cushioning effect of the spring.

Mode of operation: The said apparatus is positioned under a tree to undergo harvesting (either mass or selective harvesting). The harvested fruit falls freely into the apparatus, the weight of the fruit(s) acts as the load (force) on the springs. The spiral spring being a compression spring, squeezes together in proportion to the weight of the fruit and to a point which depends on its stiffness constant. The spiral spring resists the fruits downward movement in readiness for a rebound. But just before the rebound, the helical spring being an expansion spring stretches also in proportion to the load (fruit). Having a combined stiffness constant greater than that of the spiral spring, it quickly contracts, pulling back the spiral spring before rebounding, an act that would have pushed the fruit back into air. The aftermath of all these are that, the spiral spring gently returns to position, the fruit rests, remaining in place to be picked up bruise free. More of these apparatus can be combined to give no chance to fruits which may fall wide away especially during mass harvesting. 



The apparatus was tested for efficiency using a popular fruit, the Sweet Orange (Citrus cinensis). The average mass of the fruit is about 140g. Therefore, the apparatus with =23.33Nm-1 is appropriate. Individual fruits to be harvested were first critically inspected to ascertain the level of firmness and selective harvesting was carried out using gotohel. On harvesting, the fruit falls on the apparatus. It was picked up and thoroughly examined for bruises in comparism with earlier inspection. Similar test was repeated using same apparatus but this time with Common Mango (Mageferia indica) and Julie Mango having average masses of 90g and 155g respectively.



The outcome of the test reveals that for Common Mango, the fruit fell on the apparatus and experienced multiple rebounding and finally rested. Also, no spring noise was heard. Inspection shows several minor bruise. For Sweet Orange, it fell on the apparatus and simply rested, bruise free. For Julie Mango, a loud spring noise was heard on impact with apparatus, the fruit rebounds once and a little into air and finally rested but not without major bruises at points of impact. Table 2. Summarizes the outcome of the test result.

Table 2. Summary of test results.





Common Mango


No spring noise, multiple rebound and  fruit finally rested.

Several minor bruises

Sweet Orange


No spring noise, and fruit simply rested.                         

Bruise free

“Julie” Mango


     Loud spring noise, single

     Rebound and fruit rested                            


Major bruise at point of impact



From results above, it can be seen that a very important factor that determines the apparatus of a given  to use is the mass of the fruit of interest. As is the case with Julie Mango, with its mass being beyond capacity of apparatus, it squeezes the spiral spring to it maximum, feels the shock as it bangs the spring against the cross rod and resulting in the spring noise and a major bruise at the portion of impact. All these happen so fast, the helical spring comes to play after the harm is done only to pull the spiral spring back in place. A combination of this and the restoring force of the spiral spring results in the observed rebound. The reverse is the case with common mango having mass less than the capacity of apparatus. The fruit being too light as to depress the spiral spring enough to call for the extension of the helical spring to play its role of rebound prevention. The consequence of these is the harsh contact with the spiral spring resulting in several minor bruises from multiple rebounds. Best performance was the case when the appropriate fruit (sweet orange) for which the apparatus was specifically designed. Both the spiral and helical springs respectively played their roles of cushioning effect and rebound prevention only when the sweet orange was used in agreement with equation (8).



The bruise prevention mechanism presented above works effectively not only for sweet orange but for fruits having same average mass. For fruits of other masses, reference is made to equations (8) and (11) from where the appropriate spring constants and effective height are obtained. Its portability and ease of combination allows for this flexibility. With this apparatus in place, the menace of fruit bruise which has remained a major headache to fruit farmers around the world is solved scientifically. Thus, the world is sure on her way to fruit sufficiency.



Ibrahim A.G. (2006) Design, Construction  and Characterization of a Pseudo-Fruit Transducer. An unpublished M. Sc. thesis, Department of Physics, University of Agriculture Makurdi, Benue State. Pp 82-83.

Ibrahim A.G.,Agbendeh, A.A.,Onoja, A.D. (2006): Design and Construction of a Pseudo-fruit Transducer for the measurement of Impact Bruises on Fruits. A paper presented at the 29th annual conference of the Nigerian Institute of Physics held at University of Nigeria, Nsuka from 16th to 18th August, 2006.


Ibrahim A.G. (2009): Design and Construction of a Fruit Transducer for the Measurement of Bruises on Fruits. Journal of Science, Education and Technology. Vol 2, No. 1, pp 17-22.


Ibrahim A.G. (2009) Analysis of Impact Bruise Data of Selected Fruits. Journal of science, Education and Technology. Vol 2, No. 1, pp 51-54.


Halliday D, Resnick R, Walker J. (2006) Fundamentals of Physics. John Wiley and Sons, Inc. Sixth Edition. Pp 126.


Akinboro L.O .(1988)  Marketing  Prospect for Fruits in Nigeria. A publication of National Horticultural Research Institute. Occasional paper No. 13. Pp14.