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Scales
- 1.
- 2. Representing objects Someobjects cannot be represented in their real dimensions because they are much larger than the drawing paper. Representation on objects
- 3. Representing objects Anotherones cannot be represented in their real dimensions because they are soo small than it would be impossible to draw them with the necessary precision. Representation on objects This is a fly in its actual dimensions. But, can you see any detail? And now?
- 4. Representing objects Thesolution to this problem is to, proporcionally, reduce or amplify all the dimensions of the object. Representation on objects yes no
- 5. Scales The ratio betweenthe dimensions of the drawing and the dimensions of the actual object is called scale. Representation on objects Scale = Dimensions of the object in the drawing Dimensions of the actual object Mathematically, it´s expresed as:
- 6. Scales A scaleis, for example, 1:2. Representation on objects Scale = Dimensions of the object in the drawing Dimensions of the actual object According to the mathematical formula it means that 1cm in the drawing is 2 cm in the real . But, what does it mean? S = 1 2 S = 1 2
- 7. Scales S =1:2 Representation on objects 1cm in the drawing corresponds to 2 cm in actual object. OR 1km in the drawing corresponds to 2 km in actual object. OR 1mm in the drawing corresponds to 2 mm in actual object. OR… Because scales are ratios. It implies scales haven´t got units.
- 8. Scales Representation on objects The ratio is: 2 squares 6 squares, or, wha´t is the same, 1 square 3 squares, so, it´s reduced three times. So, the scale is 1:3 6 squares 2 squares
- 9. Scales There aredifferent types of scales: Representation on objects Reduced scale The draw is smaller than the real object Actual scale The draw is like the real object Enlarged scale The draw is bigger than the real object
- 10. Scales: reduced scale Representationon objects Reduced scale The draw is smaller than the real object It´s used to represent big objects, so they can be drawn on paper The standard reduced scales are 1:2, 1:5, 1:10, 1:20, 1:50; 1:500, …. Other not standard reduced scales are 1:7, 3:8… E:1:100 We have reduced 100 times the real size of the elephant
- 11. Scales: actual scale Representationon objects Actual scale The draw is the same than the real object It´s used to represent medium objects, that can be drawn on paper The only standard actual scale is 1:1 Other not standard actual scales are 2:2, 3:3, 59:59… E:1:1 We haven´t reduced or amplified the real size of the hamster
- 12. Scales: enlarged scale Representationon objects Enlarged scale The draw is bigger than the real object It´s used to represent small objects, so they can see them on paper The standard enlarged scales are 2:1, 5:1, 10:1, 20:1, 50:1; 100:1, …. Other not standard enlarged scales are 9:1, 14:5… We have enlarged 100 times the real size of the mosquito E:50:1
- 13. How can youwork with scales? Let´s solve this problem: Representation on objects The distance between Zaragoza and Huesca is 4 cm in the map. The real distance is 72 km. So, whay scale have we used? We´ll always follow these steps: 1. Summary the data. 2. Write the formula 3. Replace the letters in the formula with the numeric dates 4. Solve the equation. 5. Remark the result
- 14. How can youwork with scales? Representation on objects The distance between Zaragoza and Madrid is 4 cm in the map. The real distance is 72 km. So, whay scale have we used? 1. Summary the dates. DATA: Scale= ? Real size=72 km= 7200000 cm Drawing size=4 cm Notice the real size must be expressed in the same units as the drawing size
- 15. How can youwork with scales? Representation on objects The distance between Zaragoza and Madrid is 4 cm in the map. The real distance is 72 km. So, whay scale have we used? 2. Write the formula DATA: Scale= ? Real size=72 km= 7200000 cm Drawing size=4 cm S= Drawing size Real size
- 16. How can youwork with scales? Representation on objects The distance between Zaragoza and Madrid is 4 cm in the map. The real distance is 72 km. So, whay scale have we used? 3. Replace the letters in the formula with the numeric datesDATA: Scale= ? Real size=72 km= 7200000 cm Drawing size=4 cm S= Drawing size Real size S= 4 7200000
- 17. How can youwork with scales? Representation on objects The distance between Zaragoza and Madrid is 4 cm in the map. The real distance is 72 km. So, whay scale have we used? 4. Solve the equation or simplify it DATA: Scale= ? Real size=72 km= 7200000 cm Drawing size=4 cm S= Drawing size Real size S= 4 7200000 S= 1 1800000
- 18. How can youwork with scales? Representation on objects The distance between Zaragoza and Madrid is 4 cm in the map. The real distance is 72 km. So, whay scale have we used? 5. Remark the result DATA: Scale= ? Real size=72 km= 7200000 cm Drawing size=4 cm S= Drawing size Real size S= 4 7200000 S= 1 1800000 S=1:1800000
- 19. How can youwork with scales? Representation on objects 1. Summary the dates. DATA: Scale= 1:100 Real size= ? Drawing size=4.5 cm This drawing is 4,5 cm high. If we have used a 1:100 scale, how high is the real rocket?
- 20. How can youwork with scales? Representation on objects 2. Write the formula DATA: Scale= 1:100 Real size= ? Drawing size=4.5 cm This drawing is 4,5 cm high. If we have used a 1:100 scale, how high is the real rocket? S= Drawing size Real size
- 21. How can youwork with scales? Representation on objects 3. Replace the letters in the formula with the numeric dates DATA: Scale= 1:100 Real size= ? Drawing size=4.5 cm This drawing is 4,5 cm high. If we have used a 1:100 scale, how high is the real rocket? S= Drawing size Real size = 4,5 x 1 100
- 22. How can youwork with scales? Representation on objects 4. Solve the equation or simplify it DATA: Scale= 1:100 Real size= ? Drawing size=4.5 cm This drawing is 4,5 cm high. If we have used a 1:100 scale, how high is the real rocket? S= Drawing size Real size = 4,5 x 1 100 x= 100 x 4,5 1 x = 450 cm
- 23. How can youwork with scales? Representation on objects 5. Remark the result DATA: Scale= 1:100 Real size= ? Drawing size=4.5 cm This drawing is 4,5 cm high. If we have used a 1:100 scale, how high is the real rocket? S= Drawing size Real size = 4,5 x 1 100 x= 100 x 4,5 1 x = 450 cm Real size =4,5 m
- 24. How do youknow what scale to draw an object at? Representation on objects Let´s solve this problem now: You want to draw a bus measuring 5 m long an 2 m high on a sheet of DIN A4 paper (210 x 297 mm). What scale you must use?
- 25. How do youknow what scale to draw an object at? Representation on objects You want to draw a bus measuring 5 m long an 2 m high on a sheet of DIN A4 paper (210 x 297 mm). What scale you must use? Remember your bus must fit on the two dimensions, long and high. Remember that scales are ratios.
- 26. How do youknow what scale to draw an object at? Representation on objects You want to draw a bus measuring 5 m long an 2 m high on a sheet of DIN A4 paper (210 x 297 mm). What scale you must use? Divide the long of the bus by the long of the sheet, and you´ll know how many times can you reduce the bus size. = 16,83 5000 297 You can reduced your bus more than 16 times, that is, 17 times
- 27. How do youknow what scale to draw an object at? Representation on objects You want to draw a bus measuring 5 m long an 2 m high on a sheet of DIN A4 paper (210 x 297 mm). What scale you must use? Divide the high of the bus by the high of the sheet, and you´ll know how many times can you reduce the bus size. = 9,52 2000 210 You can reduced your bus more than 9 times, that is, 10 times
- 28. How do youknow what scale to draw an object at? Representation on objects You want to draw a bus measuring 5 m long an 2 m high on a sheet of DIN A4 paper (210 x 297 mm). What scale you must use? Considering the long, you can reduce the bus dimensions 17 times. Considering the high, you can reduce the bus dimensions 10 times. So, yo must reduce the dimensions 17 times E= 1:17 (If we only reduce them 9 times, it won´t fit the lenght)